Well, Marx seems to make it pretty clear in the Communist Manifesto that the ultimate form of government would be democratic, but there would need to be a period called the Dictatorship of Proletariat, where a technocratic autocracy needs to set up the economic systems. Keep in mind that Marx and Engels believed the revolution would happen in industrialized states as they stood in the mid-19th century. With the exception of Hungary’s first very brief flirtation with Communism in 1919 with the First Hungarian Peoples Republic, none of the Communist states that formed, beginning the Soviet Union, were actually industrialized to the significant extent that would have met Marx’s conditions. Both Russia and China were still primarily agrarian economies more feudal in nature, so you’ll notice that in both the USSR and China there were rapid industrialization programs to try to bootstrap the economies, and the early Communist periods attempted some degree of economic liberalization before clamping down.
The only kind of Marxism I can think of that has ever really penetrated academia is the notion of class struggle. This is where Marxist theory is probably on firmest ground, since it does explain a number of historical events like the Social Wars of Ancient Rome and the Peasants Revolt. The tendency of economists and historians up to Marx’s time was to really only look at the top end of society; the aristocracy, nobility and the mercantile classes, and basically ignore commoners and peasantry. What Marx did accomplish was to force scholars to look at society much more broadly, so history’s began to read less like “King so-and-so fought rebellions by his barons” or accounts of wars without any attempt to put those wars into any wider socioeconomic context.
That all being said. Marx’s economic theories were absolute bunk. None of his predictions came true. There were no successful workers revolts that overthrew the major capitalist states of the 19th century. Those states, by and large, either were already in the process of liberalizing (like Britain, as the House of Commons gained supremacy and voting reform acts steadily increased the voting franchise) or rulers moved quickly to integrate more workers rights into their political and legal systems, as happened in Germany with the explicit legalization of trade unions and other workers and education reforms. So the states where Communism took hold were states, ironically, not sufficiently economically advanced enough according to Communist theory. Leninism and Maoism were all attempts to explain away Communism’s utter failure in the more developed states, and explain why it was necessary in the agrarian states they took root in.