One way to organize a class like this is to start with the orthodox approach and then present the various heterodox alternatives. I don't know if that's the best way to do things; but it is what I am doing. So we divide things up:
1. Orthodox trade theory. Orthodox approaches to trade (the first half of any standard textbook; we are using Caves and Frankel) treat trade as an exchange of goods for goods. We assume that trade is always balanced and that all resources are fully employed, and show how specialization by different countries in their preferred activities leaves everyone better off. We can divide this approach into Ricardian models, which treats countries preferred activities as dictated by inherent differences in productive capacities, on the one hand; and on the other, the Heckscher-Ohlin models that regard countries as having the same productive technology but different "endowments" of (a relatively small number of) "factors of production." As far as I can tell, these two kinds of models are not associated with distinct schools of thought in any larger sense; but it seems to me that the tension between them is one of the more interesting things in the orthodox theory.
2. Keynesian approaches. Here the important thing is the systematic relationship between income-expenditure and trade flows. On the one hand, we think a predictable fraction of incremental expenditure will fall on imports, and on the other, net exports are a form of autonomous demand boosting income. The short-run version of this approach used to be fully respectable; one very good presentation is Dornbusch's 1980 textbook, Open Economy Macroeconomics.  The long-run version of the Keynesian approach is Thirlwall's model of balance-of-payments constrained growth. I don't know that this has ever been respectable but I think it's useful and sensible and, I hope, teachable.
3. New trade theory. The starting point here is that while orthodox theory says that the biggest gains come from trade between countries that are most different (in terms of productive capacities or factor endowments), what we see in the real world is that most trade is between basically similar industrialized countries. The explanation, according to this approach, is that most trade is not in fact driven by comparative advantage, but by increasing returns, which reward specialization even in the absence of any inherent differences between countries or regions. This is the stuff Paul Krugman got his prize for. One puzzle about the new trade theory is that its practitioners almost all endorse the same free-trade policy orthodoxy underwritten by the old trade theory, even though the substantive content would seem to undermine it. What the new theory says is, first, that the pattern of specialization between countries is in some important respect arbitrary and at least potentially shaped by choices; and second, that the global distribution of income is a function of who ends up with which specialty. in this sense, there is some affinity between the new trade theory and Marxist theories of imperialism, dependency and unequal exchange. I'd wondered for a while if anyone had written about this connection. The answer turns out to be yes: Krugman himself. He even cites Lenin!
4. Development, dependency and unequal exchange. There is a large body of radical theory here, which I admit I have not quite got my arms around. For current purposes, let's think in terms of two strands of analysis -- or at least two sets of questions, which may or may not correspond to different schools or bodies of theory. First, there is the relationship between trade and economic development. Historically, we could put this at the very beginning of the list, since it seems that many of the earliest writers on what we now call economics were centrally concerned with this question. But for our purposes, we are interested in the tradition that runs from Hamilton to Friedrich List to Gerschenkron to Dani Rodrik and Ha-Joon Chang. These mostly pragmatic analyses, associated politically with rising rivals to the current hegemon, include a mix of infant industry/"import protection as export promotion" arguments, and trade restrictions as devices to expand the domestic policy space (the positive side of mercantilism emphasized by Keynes.) Second, there are the various theories that go under the names of dependency and unequal exchange. The key claim here is that there is a systematic movement of prices that favors the North and disfavors the South. We may further subdivide these theories into Prebisch-Singer and related approaches, and more Marxist analyses from Hobson, Lenin and Luxembourg through Baran to Frank, Wallerstein, Amin and Emmanuel.
Another way of looking at this: Among the assumptions of the orthodox theory are that all resources are fully employed, that prices always adjust so as to balance trade (or equivalently, that goods trade directly for goods), and that countries' productive capacities can be taken as exogenous and determine the pattern of trade. Keynesian approaches reject the first two of these assumptions, the new trade theory rejects the third; the various development/dependency approaches also reject the third assumption and in some versions the first two as well.
There reason I'm posting this here is I'd like to integrate my teaching more with this blog. So the hope is to have a bunch of posts about all this over the next few months. I'm sure I'll get a lot of things wrong; maybe the readers of the blog can correct some of them.
 On the other hand, this contemporary (and very admiring) review of the Dornbusch book does chide him for starting with
a nonmonetary "Keynesian" model with rigid prices, fixed exchange rates, and unemployment ... The basic consideration is short-run full employment; long-run problems of allocation and prices are left in the background. Economists with a more "classical" turn of mind may be a little disconcerted to find tariffs introduced as instruments to raise employment and to see real wages explained by the "claims" of trade unions. They would probably prefer to start out with the long-run picture, linking monetary aspects firmly to the pure theory of international trade.
So maybe it wasn't ever fully respectable. One thing I'd like to understand better is exactly when and to what extent "Keynsian" theory was accepted among academic economists.