What do we know about the causes of global income inequality?
I have to say I do not believe in simple all encompassing answers. The reasons behind the differences are probably complex and multitude, varying from country to country. Below are some answers that one runs into and I think these probably account for a share of the inequality.


The book Why Nations Fail deals with the first question extensively. It is a highly acclaimed work (though personally I was not always convinced by their reasoning) by renowned economists Daron Acemoglu and James Robinson. Their basic argument is that inclusive democratic institutions lead to greater growth because it safeguards business and economic interests of the people.
Hence they see the biggest obstacle in undemocratic cultural traditions and lack of institutions. 
An argument I read somewhere (perhaps it was the Dictator's Handbook) is that developed countries prefer dictators in power to fledgling democracies in other countries. The reason is that fledgling democracies are not very stable, and that is bad for investment. Also dictators may be bribed more cheaply to disregard their people's best interest. (For example they may not implement environmental regulation for a price. The same may be said for democracies, but the price is usually higher.) In this way business interests in developed countries may directly contribute to dictatorships, which according Acemoglu and Robinson is what hinders economic growth.