What does Realism explain best and what does it miss? What does Radicalism explain best and what does it miss? What does Liberalism explain best...

I really like this question; it nicely emphasizes how each of these theories has merits and flaws, and the truth is best understood as some combination of them.

Realism assumes that nations act in their own self-interest, and largely ignores the internal structure of each nation. It assumes that nations act to achieve greater wealth and power, and basically ignores all other considerations. Realism is actually quite useful at explaining war; when international institutions break down and different nations end up in conflict, assuming that they will act in their own self-interest is often quite accurate. Realism is often associated with a cynical attitude that human beings are selfish and cruel to one another. What realism largely fails to explain is peace, especially when there is a clear imbalance of power as in the world today in which the US is a global hegemon. (During the Cold War, Realists could say that it was the fear of being nuked by the Soviet Union. But that doesn't make much sense now that the Soviet Union has fallen.) If the US were simply a self-interested economic agent, it would try to conquer everyone to maximize its own wealth; yet that clearly doesn't happen. Not that the US never engages in war, but warfare today is rarer and causes fewer deaths than at any other time in history.

Radicalism assumes that basically all politics is reducible to economics, and specifically to class warfare between the rich and the poor. Radicals argue that war is almost always born of the rich finding some new way to exploit the poor. Radicalism does a good job of explaining imperialism and colonialism, which really do seem a lot like ways for nations governed by the rich to exploit nations full of poor people; but Radicalism fails to explain why imperialism and colonialism are so much less common now than they once were, as well as why global poverty is rapidly declining and is now at the lowest level in history. If history were just a march of the rich exploiting the poor, how could it be that millions of people have been lifted out of poverty by globalized markets?

Liberalism assumes that nations act according to their own values, and focuses quite heavily on the internal structure of governments, particularly the question of how democratic versus authoritarian they are. Liberalism postulates that democratic nations will get along better with one another than they do with authoritarian nations (or than authoritarian nations do with each other), and that by spreading democracy we can ultimately spread peace. Liberalism is often associated with an optimistic attitude that human beings are kind and altruistic toward one another. Liberalism doesn't say that conflict doesn't exist, but usually explains conflict through misunderstanding or faulty institutions rather than the inherent selfishness of human beings. Liberalism does a much better job of explaining the trend toward global peace that has been going on for centuries and greatly accelerated after the end of WW2; as democracy spread and the democratic US became the global hegemon, the institutional structures were established to greatly reduce war. Where Liberalism comes up short is in understanding why authoritarian governments form and persist in the first place; if democracy is so great, why doesn't everyone know that? It turns out that some people really are very selfish and cruel, and a sound theory of human behavior must take that into account.

Constructivism emphasizes that states aren't actually things in the way that rocks or trees or people are physical objects in the world---they are social constructions, created by the collective action of many people. Thus, they reject the idea that nations even have well-defined "self-interest", instead arguing that nations act according to the interests and values of their people, aggregated or selected by some mechanism of government (such as a dictator or voting system). Constructivists also often focus on identity, particularly a sense of national identity that motivates people to act in the (perceived) interests of their nation. They often discuss how norms and attitudes toward identity can change over time and under different circumstances. Constructivism is clearly right about the basic fact that states are socially constructed (which Realism especially tends to ignore), but without additional insights (such as from Liberalism, the other international relations theory most compatible with it), it can often be too vague and nebulous to really be useful in predicting or changing the behavior of nations. In some ways Constructivism is more of a meta-theory than a theory per se; it places restrictions on what sort of theory makes sense---anything ascribing motivations directly to nations is suspect---but doesn't make detailed theoretical predictions on its own.