Marxism has an influence in academic study far beyond economics and political economy, especially as social science has split into separate disciplines such as economics, political science, sociology etc. It retains more of an influence in the social sciences outside mainstream economics, as well as in various heterodox schools of economics. Its strength lies in its inter-disciplinarity and in its ability to endogenise factors normally considered exogenous, unexplained or ‘outside’ the system under scrutiny, whether that be the economy, society or polity. Thus potentially more can be explained and in a richer fashion, although it can also potentially be more wrong in its explanations of phenomena.
With Marxism as a basis for study, elements of economic, social, political and cultural life can be examined, with the mode of production, whether feudal, capitalist, or socialist, as a key influence on the potential outcomes of these aspects of life. It can sometimes be accused of economic determinism, such that the mode of production and materialism are seen as the dominant forces shaping them. For socialists, numerous economic, social, political or cultural ills are seen as the product of a capitalist mode of production which needs to be overthrown and replaced with socialism. This economic determinism is argued by many to be reductionist, and although the forces of material life are important, they should not therefore be seen as the only ones shaping all aspects of life. This is taken furthest by theorists espousing the philosophy of over-determination, such that everything causes and is caused by everything else, and narrower aspects of causalities are chosen consciously and in some sense more honestly, with particular goals in mind, whether they be social revolution or otherwise. Over-determination has been discussed in a previous post, so all I will say here is that it need not require Marxism to be the only method of theorising, and I find that the conscious choosing of particular aspects of an over-determined complex reality intellectually empowering.
In sum, Marxism remains a potentially fruitful method of study across various fields, and over-determination can be a way in to such study.