My good friend and co-author John Judis has an excellent review essay in the new American Affairs where he addresses this question in the process of reviewing two newish books, Erik Olin Wright's How To Be An Anti-Capitalist and Bhaksar Sunkara's The Socialist Manifesto. The essay has a very useful discussion of what on earth do we really mean when we use the word "socialism" and what is or should be the relationship between socialism and Marxism.
"Today’s young socialists, many of whom were born after 1989, no longer think of Soviet Communism as socialism. But at the same time, many don’t share a clear alternative conception of what a socialist politics should consist in, or what socialism itself might look like. In explaining his democratic socialism, Sanders invokes Franklin Roosevelt’s New Deal and Scandinavian social democracy. Kuhnert and the DSA socialists embrace a neo-Marxist socialism that would abolish the capitalist class. That raises the question: is socialism, as currently conceived, a stark alternative to capitalism or merely a symbolic rebuke to the prevailing values and practices of capitalism—or is it something in between?
There is at present no correct answer to this question. The answer will have to come out of movements, campaigns, and candidates. It will also come from attempts by theorists to articulate and propose what a socialist politics and socialism itself should look like in the twenty-first century. Here I want to look at two recent efforts to imagine a twenty-first-century socialism: a sophisticated analytical account from the late American political sociologist Erik Olin Wright, and a more engaged offering from Bhaskar Sunkara, the founder of Jacobin and a leading light in the DSA."
"Today American socialism is not a fixed idea but an expression of deep dissatisfaction with what are seen as capitalism’s values and practices. It is hard to imagine, as Marx and Engels did in the Communist Manifesto, a clear path from capitalism today to a socialist future. But it is helpful to understand, as Wright has contended, that the seeds of an alternative America can be—and, to some extent, may already have been—sown within American capitalism."
Fair enough, though what Wright is essentially advocating is an advanced mixed economy with socialist characteristics. But I'm OK with that.
For extra credit, you could take a look at Alec Nove's classic The Economics of Feasible Socialism. This will help you think--really think--about what socialism has been and what it could reasonably ever be.
For extra, extra credit, you could also look at Mario Nuti's enormously long but extremely informative The Rise and Fall of Socialism that includes an exhaustive typology of different forms of socialism that we have seen over the years. Nuti, incidentally was a collaborator of Nove's.