To get the negative point out of the way first: I wish that the book had been longer and had covered more cases of unrecognised states in greater depth. She concentrates on the classic Eurasian frozen conflicts (the Caucasus Three, Transnistria and Northern Cyprus), the classic partial recognition cases of Kosovo and Taiwan, and also looks at Somaliland and the failed cases of the Republika Srpska Krajina and Tamil Eelam, which went down to defeat by Croatia and Sri Lanka respectively in 1995 and 2009. I wished she had found more space for the Bosnian Republika Srpska, which is the only one of these territories I myself have lived in, and I thought also that she missed the interesting interval in the early 1990s when Macedonia, despite fulfilling all the criteria required of it by international law, was none the less not recognised by the majority of international players, a situation that lasted shamefully longer than some like to remember. She also mentions the similar cases of Montenegro, Bangladesh and Eritrea in passing, and I would have liked more detail. Essentially my biggest criticism is that I liked it so much I wanted there to be more. But I appreciate that for the author, enough is sometimes enough.
Caspersen makes the important point that the problem of unrecognised states has arisen only in the last sixty years or so. Before the second world war, it was sufficient to win your war of independence, hold your territory, and then send out your ambassadors in the reasonable expectation that they would be received. Since then, however, the international system has become wedded to the doctrine of inviolability of frontiers, which I think demonstrably has reduced the number of casus belli in the last half century, but which doesn't offer an easy get-out for when recognised states break down and fail to discharge their obligations to their citizens. Unrecognised states nestle in the grey zone between self-determination and change of borders. International organisations, which are really where you get to go to prove you are playing with the big kids, formally are groupings of states which all recognise each other and are therefore unlikely to make speculative recognition of someone whose territory is claimed by someone else within the system. Postmodern idealists like to mumble about how shared sovereignty or partial sovereignty could be an answer, but really this is too subtle a concept to be usefully deployed in most cases; you're either recognised as sovereign or you're not, in most policy-makers' minds and therefore in most people's reality. (Where these concepts work, and this is a point Caspersen misses, it is because the autonomous region is given large autonomy not only in areas of coercion, ie control of their own security forces, but also in areas of culture, meaning use of languages, flags, symbols and names of government institutions.)
The real strength of this book is that, rather than treating unrecognised states as untidy and problematic bits of international relations which the grownups need to clear up, Caspersen takes them on their own merits as subjects in their own right - sure, they are often beholden to powerful external patrons, but that doesn't mean that the patron calls all the shots (and in fact I can't think of a single example of a totally subject puppet state, since South Ossetia has twitched into life and the Russians are trying to ditch the Transnistrian leadership); sure, they are sometimes institutionally weak and badly governed, but that is often equally true of recognised states (indeed, in the case of Somaliland, the parent state is functionally non-existent and it is the unrecognised seceders who have actually built a viable polity). Caspersen has some very interesting analysis of why the more successful unrecognised states have adopted internal democratisation as a means of adding legitimacy to a government which is denied legitimacy by external actors.
Caspersen's key point relates to engagement with the government and citizens of the unrecognised state, particularly by the "parent state" from which the unrecognised state has seceded. Isolation is easy, and of course if the strategic circumstances turn out right can be a good precursor to the military defeat which is the most frequently encountered fate of unrecognised states, with all its awful human costs. Economic and person-to-person engagement carries risks for the parent state, in that it may appear to recognise the status quo of the separation and to legitimate the social structures (and by implication the political structures of the seceding state. But it carries even more risks for the seceding government, an essential part of whose narrative must be that life with the former parent state is impossible; as far as I can see, it is very much worth the parent state's while to engage in that way (and I would observe that the cases where I see conflict as least likely - Taiwan, Transnistria and Northern Cyprus - are precisely the cases where despite the conflict strong economic links have been fostered by both sides). If a peaceful settlement one way or the other is the preferred goal in a particular situation, serious engagement across the boundary without prejudice to future status is a key stepping stone in that direction. It's an argument that almost shouldn't have to be made, but Caspersen provides a great deal of evidence for it.