Right now there seems to be a huge amount of obfuscation and misinformation about this. I imagine it is fuelled by party politics and socialist is equated with Labour in the UK and Democratic Social Justice Warriors in the US. This is like being a fan of football in general versus supporting a team. Socialism is a lot more than just supporting a team, it is a theory with a history just like football itself.
I have never read Marxism, but I read his predecessor Hegel who I consider superior. The key thing to grasp is Dialectics. Dialectics is nothing to do with Socialism. It has its roots in Ancient Greece, is present in Chinese Daoism (yin-yang) and in Indian thought too. In a sentence it is the unity of opposites, which sounds absurd at first glance.
IN non-dialectic (dualistic) logic you have things that are true and things that are false. This coiled thing in the shadows is either a snake or it is not. The defendant is either guilty are they are innocent. The man in the film is either a good guy or they are a bad guy. The dice is either a six or it is not. It is a simple world divided into black and white.
Quantum physics says the world isn't like this. The dice can be both 1 and 6 at the same time, the cat can be both alive and dead. This is not dialectics however.
In the film Heat (which I haven't seen) you have the Good guy (De Niro) and a Bad buy (Pacino). I imagine the reason for the famous scene is that actually they are identical people. They are both tenacious, smart and out to win. It is less a cop and a gangster and more a boxing match. De Niro has good qualities, but so does Pacino. De Niro has bad qualities and so does Pacino. But to be real dialectics De Niro's good qualities should be there because of Pacino Bad qualities and vice versa. Not having seen the film I cannot comment. But suppose Pacino had made a vow to avenge the death of his brother who was killed ruthlessly by De Niro. De Niro may have been a cop, the good guy, but his lack of compassion led Pacino into a situation where he had to take revenge (assuming revenge and honour are ever a good thing). The result is that look one way De Niro is good and Pacino the gangster, look the other De Niro is ruthless and Pachino the devoted brother. And the more they struggle the more they get intertwined, the more the coffee and cream mix until they are inseparable. But if either side quits the whole things disintegrates into nothing. This is dialectics. But coffee never blends with cream in dialectics it is always opposites pushing against each other. A simpler example might just be a suspension bridge where the weight on both sides of the tower keep it balances. If either side fails the whole thing fails. Opposite forces in equilibrium, while opposites, there is no winner, no right one and if either fails the whole thing fails. A famous examples is light and darkness. No light then there is no shadow, but no darkness then how can you switch the light on. Light is married to Darkness they are inseparable. Indeed looking at darkness you can almost see the light they are so interdependent. I once had an absorbance trace where I entered into a ring of light from an over head lamp. I forgot about the darkness that must have been there to make it into a ring. But when I suddenly became aware of the ring shape of the light my mind stepped over a threshold and absorbed into the infinite darkness, which was however fully illuminated. Impossible to describe unless you experience it (Jhana 6 - there are books on it). This is ultimate profound dialectics.
So what has Dialectics to do with Socialism. Most socialism is based upon a Historical theory which describes the progress of mankind from primitive to advanced and the process is dialectics. It is a beautiful theory, because it employs dialectics, and gives great insight into history. In Hegel the key highlight is the transition from Master/Slave to Absolute which in Marxism is the transition from Capitalist to Communist. Dialectics ends at this point in both versions. I personally don't believe that Dialectics ever ends. Following Buddhism Dialectics never ends because it never started, it is an illusion caused by ignorance. Unlike Hegelianism I believe the Absolute is always available, and the path is not a prescribed as it is in these Systems. Never-the-less the broad ideas are of great interest. Master/Slave is the transition of mind from Kings and Servants where Kings are entitled and Servants look up to their master to Servants taking that freedom they saw in their Master for themselves. This fits the historical events of the C18th revolutions where the mass no longer tolerated having a superior class and took freedom for themselves which we call Capitalism.
Capitalism however has its flaws and the freedom of the revolutions was soon seen to be limited. Wealth grew as once humble servants moved to cities to make a life for themselves, taking up home in houses built by factory owners and increasing their wages. But there was a down side because it meant a whole class giving up their traditional lifestyles and lands and becoming dependent on the factory owners. Redundancy became a constant fear. Once you lost your job you had nothing and you couldn't return to farming because your land was all sold up and machines were now farming it. Economics was against people also as capitalist classes knew how to keep wages down and increase their profits. Poverty rather than going away became worse.
And so Socialism was born. The reaction to the poverty that emerged from Capitalism. From the Hegelian and Marxist theories people expected a Communist revolution to overthrow the wealthy capitalists just as the C18th revolutions had overthrown the Kings and Aristocrats. But it never came. Russia and China being very late to the party tried to skip straight from Feudalism to Communism missing out Capitalism but the theory never said this was possible, and they ended up going toward Capitalism anyway. But despite all the propaganda that was touted around, both Russia and China did successfully liberate their people from the oppression of the aristocratic system just as England tried in the C17th and France in the C18th. Even America had to overthrow its Aristocratic rulers in an Independence struggle. And many other countries followed suit in a wave of revolution from Imperial Aristocratic rule after the war. A problem for the British is that while most of the world has now been liberated from Feudalism and Imperial rule there is the possible fact that the British still remain governed by a ruling aristocracy. Perhaps here in UK, the mother of Socialism, we still haven't made it to Capitalism!
So Socialism is a complex mix of ideas, including a view of history and social change and human evolution. It is a reaction to the poverty and injustice of Capitalism and Industrial Revolution and not a single political movement that sets out to oppose other movements dualistically. It does at its heart have dialectics anyway, so that for its own perspective it sees humans intertwined in an historical struggle of progress. What a far cry this is from the dualistic view that is common at the moment which sees Socialism as the Red Corner in a boxing match with other systems. I've always felt this view is a hang over of the cold war where the US Pentagon hatched a propaganda campaign to justify its hostility to competing post war powers.
Is Socialism still relevant as the world progressively becomes richer, poverty is reducing and happiness indexes increasing. Is there a need for any criticism of Capitalism? Isn't everything okay?/ And was Marx wrong that actually there is nothing after Capitalism?
In two words who knows. But such an argument could have been had at any point in history. After we discovered fire we could have just sat back and been happy. There remain big problems with Capitalism that cannot go away because Capitalism is flawed. Whether we work to fix those problems, or not is up to us. Marx and Hegel say that History will inevitably move toward perfection. I'm less deterministic. But I do think that things never stay the same for long, and change will happen.
The key problem with Capitalism is that no matter how wealthy we become, no matter how cheap things become and no matter how efficient our machines are some people will be owners and some people will not. And under the rules of Capitalism is you are an owner then you can rent things to those who are not owners. This means that under Capitalism some people who do not have, will be paying money to those people who do have. This is the same aristocratic system of entitlement by some over others that we fought to end. Nothing has actually changed. If we are happy with things now, then why were we not happy under Feudalism giving 50% of our produce to the land owner? Capitalism is in its heart is unequal and flawed and simply cannot survive indefinitely. The only way we can tolerate this is by apathy. Obviously those who benefit from the system will encourage apathy, which is what I believe books like "End of History" by Francis Fukuyama are really motivated by. If we really seek progress, and we adopt the thinking of Socialism, we will be looking toward a future where all humans are respected by a system which does not from the outset create division and inequality. This is not to say that we each get given 1 potato and a cup or water each morning by a central state as some satirists like to suggest, but it does mean that we do not apathetically accept a system like this where those with plenty to excess can exploit those who have only a little.
I'm not one for bloody revolutions. This is why I like Hegel more than Marx and why I prefer Buddhism to both. Revolution happen in the mind, not on the battle field. People have always been fighting (since the farming revolution anyway) but it is what they have been fighting about that has changed, and not everything they fight about is hatched in battles. Battles are for show, but the battle for ideas is quiet and far more wide reaching and powerful. Leave the battles to the duellists (dualists)... unlike Hegel and Marx I do not think History is written in blood. Lasting history is written in pubs, and over dinner tables and cups of tea (or coffee if you are Georgian or American). So the challenge still exists to solve the problems in Capitalism that were first noted in the late 1700s and which remain largely unresolved...
It is probably worth addressing one of the great Pentagon pieces of misinformation: Socialism's body count. In particular Mao, Stalin, Hitler and Pol Pot. The first thing to note is that civil wars and revolutions tend to be bloody regardless the politics. Probably the bloodiest revolution in history was the English Civil War where 1 in 6 people lost their lives. This was long before even Capitalism had been thought of let alone Socialism. And Iraq is a recent example of how civil wars, even moving toward democratic capitalism, are costly: 1 in 18 died in that war. If Stalin, Mao and Hitler are to blamed for their body counts then so must George Bush for Iraq, the various presidents behind Vietnam and Oliver Cromwell who presided over the biggest body count of all. Obviously China and Russia are massive countries and you don't compare death per death, but rather the chance of dying during the crisis. And then there is Hitler. The fact that the Allies waged a war of total destruction against Germany always seems to be forgotten. I think Germany could have been running the most successful democratic capitalist country at the time and the body count would have been exactly the same given total national destruction. This is the elephant in the room of those war statistics. The allies refuse to acknowledge the impact of the 1942-45 invasion period and the millions it killed. Now this is not to say that the Cultural Revolution, Pol Pot's killing fields, French Reign of Terror, Stalin's 2 years reign or terror were not complete disasters, but it is to say that they were not much to do with Socialism and a lot more to do with revolutions and civil wars.
18/10/2018 update
In the account above I completely ignore aufhebung. Where the East and West diverge is in the meaning of contradiction. In the East it is suffering: the dualistic divided mind is in a state of instability and suffering, but like the West this state of suffering keeps the mind searching endlessly for salvation. That perfect peace comes with Enlightenment and Liberation from dual conditional existence (either this or that, self and other) and is a return to the centre of the wheel upon which mundane existence and suffering turns. In common with the West the soul is endlessly restless until it finds peace. However in Hegel and Marx this struggle becomes a powerful and violent force that drives progress and history, taking individuals and mankind from primitive to greater and greater states until opposites are all overcome and a grand Absolute is achieved that subsumes all that has previously been troublesome and in conflict. In Hegelian and Marxist Dialectic this struggle between conflicting ideas resolves in aufhebung and the dramatic reconstruction of the rules of the game into a new world where the previous problem is now in harmony: the dawn of a new era which can be, and is, on a personal and global level... altho personal vs global is itself an ancient dialectic in need of resolution. So while the West almost justifies its violent and bloody history as a path that leads to perfection, in the East suffering is of no value and does not lead to any path except in so far as to motivate the suffering ignorant soul away from self-satisfaction. True we cannot rest until we are enlightened, but the goal is the ending of suffering rather than soldiering through the suffering as tho it is laying down a stairway to heaven. To return to the post question directly: Socialism includes all this enquiry and is a continual path, it is far from the straw-man that is popularly burned by masses who are brainwashed by an elite to believe that they already exist in utopia and whose minds are dulled by such mental opium.