Economic explanations for income inequality across nations have changed a lot. Easterly does a good summary, but basically people used to look at things like capital (ie, Rostow big-push) but then figured out that sometimes countries don't attract capital because they're poor, rather then being poor only because of a lack of capital. The search moved on to deeper causes of poverty, such as quality of institutions and policies, development of human capital and productivity, and political issues like violence.
Now, some people are looking at the underlying dynamics of why those things happen. Galor has an interesting scheme in which populations under Malthusian pressure gradually change their value structure to become more market-biased, and Gregory Clark claims that genetic and cultural changes lie behind Europe's economic dominance. Other folks at Brown have come up with some research which traces the population heritage of different groups, finding strong historical presistance for generating income.
This intersects nicely with other population genetic research. Heckman has done a lot of work on the technology of skill formation, finding that the amount of skills you can build up when early determines a lot about your future. So while everyone faces similar incentives to pursue education, people have differing abilities to do so, so you get income inequality. A major cause of population differences is time distance from agriculture. Groups that have been settled for a long-time look very different from groups that just picked up agriculture, the the latter groups have a very very difficult time adjusting--in terms of building up a tolerance to alcohol, for one.
There are a few issues with this picture:
1) How do the underlying cultural/genetic population parameters intersect with broader political themes? Presumably South Chinese populations across Hong Kong, Macao, Taiwan, Guandong are similar, but different largely exogenous political changes had very, very different results. But often, political institutions are built from other grassroots pressures, and interactions are complicated.
2) Why is this historically a bad predictor? If you go back thirty or fourty years, you see African countries living in a Malthusian environment where a high disease burden keept income relatively high above subsistence level. Post-colonial growth wasn't bad, while poverty was really concentrated in East and South Asia. Latin American countries weren't doing bad either (Argentina was one of the world's richest countries at one point) despite having a large population with minimal state history. Then things changed and historical stereotypes started to look like they have some relevance.
3) Among populations with similar experience in State-building, why is there so much variance? Mesopotamia/Egypt have a very long history of urbanization, while in England Romanization was very weak and the real state-building happened much later. But England made the transition into a Neoclassical economy first, and presumably carried the spillovers to other nearby northern European states with similarly short development history. The Mediterranean region, which is where you have the long state histories, still remained a backwater. So even within Europe, there are a lot of political/technological confounds. You can start to explain some of this by soil degration and salinity; early Mesopotamians destroyed the land so Persia and Greece became more important; and so forth until gradually the seat of power moves further north and west away from the site of initial agriculture, but this really adds to the complexity. This is also specific to irrigation-based technology for certain cereals.
Once you expand outside Europe, things get even trickier. China of course has a great long history of technological innovation and highly capable state formation, and rice cultivation with effective fertilizers kept soil productivity high. Income, however, lagged up till a few decades ago even the poorest of African nations. Catch-up growth has been significant, but that was not the only way it could have gone. India also has a very long state record, but the parts of the country with the biggest heritage in that direction are also some of the poorest right now. The point of much of this research (also Jared Diamond) is that you can kind of predict the important countries from 1500 and also some relative rankings since history matters, but this alone doesn't tell you why Europe and Japan have done well, and not Persia or Turkey. Explanations that try to do this (ie, Diamond's argument that Europe is near a lot of water) look pretty ad hoc.
4) Non-linear post agriculture histories play some part in this. For instance, many tribal people in India have known about agriculture for a long time, many are agriculturists, and all are in symbiosis with other settled groups. But they're not the same as either other agricultural groups or the more isolated groups such as the Senitalese. In India, long periods of political violence and a general lack of centralized authority (as well as whatever the effects of caste may be) probably kept the population in less of a "settled" mentality than other parts of the world. But it was still more prosperous in aggregate historically than places which only recently have seen wealth, say Eastern Europe.
5) Supply-side responses dominate how much money you have only recently (and maybe not even now). Brute force has generally been much more important.
6) Most likely, population parameters established through cultural and genetic selection determine cognitive and non-cognitive skills (The non-cognitive skills--persistence, motivation, learning to follow orders, etc. are pretty underappreciated and possibly more important). In a country like America, which is a pretty meritocratic place, you can look at the population's wealth share for a rough guide of the "potential" income (selection effects on immigrants and other historical legacies are important here too). You can look at Mauritius and Singapore similarly. Relative ordering may be fixed within a country, but explaining difference in average levels of income, even holding population composition constant, is a good deal about various geographical and political factors. In the long-run, a country's politics should respond to keep income at potential, especially in a competitive international environment, but this can take a while.
The slow rate of response of human labor to the demands of a commercial economy generates rents for the people who catch up. Capital is pretty elastically provided, so interest rates are pretty similar across time, but it's much slower to get a skilled human supply-side response, so some people collect substantial rents and you see a lot of inequality.