Is Marxism relevant today? Explain.

Marxism is fundamentally a diagnosis of the problems with Capitalism. Many of the problems that Marx originally identified still exist today, and some might argue that some of the those problems are more pronounced now than they were in Marx's own time.
For example, Marxism proposes that in a Capitalist system, the working classes are exploited by and for the benefit of the upper classes, and that this exploitation leads to a situation where the gap between the rich and the poor increases. Marxism proposes as a solution to this problem a more equal redistribution of wealth.
This idea is certainly still relevant to the modern world. Indeed, it was only in 2011 that huge protests took place around the world, most notably the "Occupy Wall Street" protests. A slogan of these protests was, "We are the 99%," which alluded to the fact that 1% of the world's population own approximately half of the world's wealth. The protestors positioned themselves as the 99% who were campaigning for a more equal distribution of global wealth. This is a fundamentally Marxist demand.