What do we know about the causes of global income inequality? According to the IMF, the GDP per capita in the USA is about \$57,000 per year. In many central African countries the figure is more like \$500 or less. These examples are indicative of the incredibly broad spectrum of levels of development observed globally.


What is the state of the art as far as economists are concerned in explaining where these income disparities have come from? Why have countries like the US grown so much quicker that those of central Africa?
What do we know about the prospects for closing this gap in the future? What are the main prerequisites for very poor countries to begin to grow quickly?
Is there a sense in which developed countries could be said to be perpetuating global inequality (for example, via unfavorable trade policies), or is the state of the developing world largely independent of "the West"?


Three questions, but I think they are fairly closely related (in the sense that the answer to 1. might well also answer 2. and 3.) so I am asking them all together here.
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.