So, this is not as detailed as others may post but I do think it is important to point out: Marxist historians and Marxist interpretations of history are relatively old fashioned. While there is definitely some credence to academic Marxism influencing a lot of historians in the 60’s and 70’s, historians have found new and interesting approaches and methods to carry out their work. This is not to say that Marx or class struggle are not useful ways to think about history still, just that there are less historians trying to identify the exact class struggle throughout history as outlined in the “Communist Manifesto”.

But to your question, what are some of these new approaches? Well, Marxism has a slight problem of breaking down the world into two basic categories: those who own the means of production (land for most of human history) and those who do not (usually - though by no means always - agricultural peasants of some type). This is...a bit reductive. As such, in the 80’s and going forward some historians sought to study and catalogue the everyday lives experience of those who are not elites or powerful. This is called Social History, and it looks to examine peasants and laborers as more than just their jobs: what did people do to pass time, how is the family functioning, the ever present question of sexuality, that sort of thing.

A subgenere of Social History that became a field all its own is called Microhistory. This method closely examines a very tight collection of sources to explore single events or small circumstances that can still answer some of the ‘big’ questions of history. The flagship example is Carlo Ginsburg’s The Cheese and the Worms which is about the inquisition trial of a Venetian Miller in the early modern world. I highly recommend it if you are curious for new approaches to history.

As an exact opposite to microhistory there is of course the Annales school famously helmed by brilliant historian Fernand Braudel which ignores all those smaller events (like wars) as “bubbles in the sea” to examine the real driving forces in history: grain prices, climate, and cash economies in agricultural communities. The Braudelian approach is favored by those who still read Karl Marx but don’t really want to waste a lot of time fitting 15th Century English peasants into the dialectic.

These are some of my favorite approaches, but there are many more that I’m sure others will share.

I think we must look into the question of 'other ways to look at history'. Marxism is idiosyncratic in its comprehensiveness. It is a system of thought that aims to explain every historical event through its systematic materialist analysis; through the prism of class struggle, alienation, exploitation etc. Marxism has one big big claim - that it can answer every historical question:

'The history of all previous societies has been the history of class struggles'

This explains its appeal; Marxism answers all the historical questions we have had. It has given its adherents a total system which explains the world in its totality. It even informs how we should live within the present, giving us the tools with which we should act in regards to the historical interpretation Marxism supplies:

“Without Revolutionary theory, there can be no Revolutionary Movement.”
― Vladimir Lenin

To answer what contrasts with this? Well, crucially, historians no longer have faith in theories like Marxism that claim to explain history in complete totality. Even less so in ones that have claim to inform how one should act in the present. It is less that new theories have come in to replace the holistic Marxist interpretation, but rather that historians have moved on from looking for an 'approach' that explain everything. Hence these approaches that you rightly see as contrasting Marxism are not necessarily a theoretical equivalent to it. They are instead a myriad of useful theoretical tools that are more specific and specialised to certain historical enquiries the historian has. For me, Michel Foucault epitomises this, seeing his work as a:

‘tool-box which others can rummage through to find a tool which they can use however they wish in their own area’

Now many would see this as a 'Post-modern' approach, but in reality it is not a comprehensive or coherent group of tools to use. These approaches are not nearly as 'neat' as Marxism in that few of them create a system so holistic. Hence I would say that the 'Marxist approach' has not been replaced with alternative approaches, but rather has been left behind in the sense that most historians no longer 'look at history' in a Marxist sense at all. They instead employ a variety of historical techniques and approaches as relevant to the specific enquiry they want to explore.

In my field of Japanese history, the most prominent school that operated counter to or in opposition to Marxist interpretations of history in the postwar era was Modernization theory, influenced by liberalism in general and Max Weber and Talcott Parsons in particular. Marius Jansen (Princeton) was one of the most prominent U.S. scholars who operated in this mode. You can find detailed discussions of this approach online, but in general, it assessed the rapid industrialization and Westernization of non-Western countries as a form of universal progress. Modernization theory was, IMHO, closely aligned with the interests of the state and with global corporations, so was not particularly attentive to authoritarianism, widening economic gaps, and social justice. Having said that, I knew Marius Jansen and he was a brilliant scholar and a lovely man.