Avian parents and social insect colonies are victimized by interspecific brood parasites—cheats that procure costly care for their dependent offspring by leaving them in another species' nursery. Birds and insects defend themselves from attack by brood parasites; their defences in turn select counter-strategies in the parasite, thus setting in motion antagonistic co-evolution between the two parties. Despite their considerable taxonomic disparity, here we show striking parallels in the way that co-evolution between brood parasites and their hosts proceeds in insects and birds. First, we identify five types of co-evolutionary arms race from the empirical literature, which are common to both systems. These are: (a) directional co-evolution of weaponry and armoury; (b) furtiveness in the parasite countered by strategies in the host to expose the parasite; (c) specialist parasites mimicking hosts who escape by diversifying their genetic signatures; (d) generalist parasites mimicking hosts who escape by favouring signatures that force specialization in the parasite; and (e) parasites using crypsis to evade recognition by hosts who then simplify their signatures to make the parasite more detectable. Arms races a and c are well characterized in the theoretical literature on co-evolution, but the other types have received little or no formal theoretical attention. Empirical work suggests that hosts are doomed to lose arms races b and e to the parasite, in the sense that parasites typically evade host defences and successfully parasitize the nest. Nevertheless hosts may win when the co-evolutionary trajectory follows arms race a, c or d. Next, we show that there are four common outcomes of the co-evolutionary arms race for hosts. These are: (1) successful resistance; (2) the evolution of defence portfolios (or multiple lines of resistance); (3) acceptance of the parasite; and (4) tolerance of the parasite. The particular outcome is not determined by the type of preceding arms race but depends more on whether hosts or parasites control the co-evolutionary trajectory: tolerance is an outcome that parasites inflict on hosts, whereas the other three outcomes are more dependent on properties intrinsic to the host species. Finally, our review highlights considerable interspecific variation in the complexity and depth of host defence portfolios. Whether this variation is adaptive or merely reflects evolutionary lag is unclear. We propose an adaptive explanation, which centres on the relative strength of two opposing processes: strategy-facilitation, in which one line of host defence promotes the evolution of another form of resistance, and strategy-blocking, in which one line of defence may relax selection on another so completely that it causes it to decay. We suggest that when strategy-facilitation outweighs strategy-blocking, hosts will possess complex defence portfolios and we identify selective conditions in which this is likely to be the case.