Capitalism and Slavery is one of the seminal works on modern slavery and its relationship to Capitalism.

Many historiographical traditions saw slavery as a kind of throwback to pre-Modern social and economic institutions and not a part of Capitalist development as such. Marxists in particular tended to use a narrow definition of Capitalism (based on wage labor) which painted Modern slavery as a pre-Capitalist survival within the development of the Capitalist system.

There was a lot of pushback against this position, especially among historians in the Americas where Modern slavery was often a predominant socio-economic institution. They tried to demonstrate that Capitalism wasn't just some oddball survival in the transition towards mature Capitalism but instead an organic institution which was key to Capitalist development and which meshed perfectly well with the rest of the system.

In the case of Cuba, Williams influenced historians like Manuel Moreno Fraginals (El Ingenio) and Jorge Ibarra Cuesta (Varela El Precursor. Un Estudio De Epoca), who both saw the planter class as part of the broader Capitalist class.

The highly influential Immanuel Wallerstein has also incorporated the position that slavery is not an incidental survival. In fact, he takes the ball and really runs with it, stating that wage labor is typical for the 'core' of the Capitalist system while non-free forms of labor, from slavery to indentured servitude, peonage, etc., are typical to peripheral parts of the system.

Many recent historians, like Sven Beckert (Empire of Cotton, 2014) and Edward Baptist (The Half Has Never Been Told, 2014) have also argued that slavery is a perfectly organic part of the Capitalist system. They recently published a new compilation of articles, Slavery's Capitalism: A New History of American Economic Development (2016) which defends this view.

The problem for Marxists is that Marx' definition of socio-economic systems rested on the dichotomy between proletarians (wage laborers who didn't own the means of production) and Capitalists (who used Capital and legal ownership of the means of production to extract surplus value from the labor of proletarians they employ). If proletarian classes are also central to Capitalism, then Marx' definition doesn't work. I'd also note that many of the authors I describe as having assumed Williams' premise often fail to give a clear definition of Capitalism or clarify this issue entirely. It is still a point of contention, as demonstrated by the fact that its authors feel the need to make these arguments so forcefully in 2016 (ie. it isn't received wisdom just yet).

In short, what do historians think of his work? I can't speak to his writing on the British West Indies, but the underlying premise of his work, attesting to the intimate and non-contradictory relationship between Capitalism and slavery, has had far reaching significance. It should be read as a really important, though no longer up-to-date, precursor of this contemporary historiographical discussion.

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PS

The book itself is also really well written and touches on interesting topics, so I'd definitely recommend reading it.