Political institutions are far more important than geography or culture to explain economic progress, according to AR. Examples include the diverse fortunes of East and West Germany, North and South Korea, or the city of Nogales (at each side of the border in the US and Mexico). Each pair shares geography and culture, but not institutions.
Other very interesting themes in the book are the exaggerated role that some academic advice gives to experts (I have sympathy for the arguments of the authors on the false ignorance of elites); the need for a certain level of centralization so that the there is a minimum amount of order and security; and the fact that the independence of colonies was not accompanied by a change in institutions and social structures.
A related phenomenon explained by AR is the reversal of fortunes in former colonies: lands that were rich in resources 500 years ago induced extractive institutions from colonizers, whereas poorer lands facilitated importing metropolitan institutions or the setting up of institutions where colonizers had increasingly equal rights. In their previous econometric work (with Johnson) they instrument poor institutions by settler mortality, thus obtaining an exogenous source of institutional variation, apparently fixing the endogeneity problem.
Reviews by Diamond, Subramanian, and Sachs have been critical with "Why Nations Fail." The polymath Jared Diamond accepts that institutions are important, but good institutions are concentrated in countries with a temperate climate, with access to sea (AR's response to Diamond and his replica are here). Jeffrey Sachs argues that contrary to the arguments by Acemoglu and Robinson, Nogales actually shows the importance of geography (being close to the US border; Mexican Nogales has ten times the size of US Nogales).
Subramanian shows graphically how China and India (the two most populous countries in the world) do not fit with the positive correlation between inclusive political institutions and economic growth. The response by Acemoglu and Robinson is that India has not been an inclusive democracy, and China will eventually decline. Other published reviews by William Easterly, Francis Fukuyama (Easterly and Fukuyama are both happy that AR address the big issues of development and institutional change instead of only minor issues common in recent research, such as the relationship between foreign aid and mosquito bed nets) and Martin Wolf are more laudatory, but also mention that AR simplify too much and too easily jump to conclusions in their book.
Relatedly, evidence on settler mortality used in their academic work by ARJ is disputed by Albouy in the American Economic Review (AER): he claims that the data used by ARJ is not representative of settler mortality during colonization and the results (that good institutions cause economic development) are not robust to the correct interpretation of the data. The response by ARJ can be found in the same issue of AER.
Earlier doubts about the research program devoted to finding clear links between specific institutions and economic development were raised by Chang (this article triggered a heated academic debate, which can be followed here) and Clark.
Institutions are increasingly seen as important as can be shown in studies about the lasting effects of old institutions (such as the Mita in Peru, the Habsbourgh Empire and land contracts in India), as surveyed by Nunn. Branko Milanovic’s work on increasing inequality between countries is consistent with this view.
Institutions are probably important especially because they support exchange when the quid and the quo are separated in time, and promote cooperation and coordination in solving collective problems, which often involve dilemmas between equity and efficiency. But institutions are not easy to define, which makes falsifying theory difficult. Additionally, institutions are not good travelers, are costly and endogenous; are not the only determinant of growth or development; and co-evolve together with outcomes, random events, preferences and the environment. You cannot just inject good formal institutions in a country and expect it to suddenly become the paradise. AR, in their fascinating book, are right especially in one thing: solutions are never apolitical. If you want to change things, you should be ready to get involved in collective action, fail and stand up again.