Coevolutionary dynamics allow revealing ongoing microevolutionary processes and adaptations. Interactions between obligate avian brood parasites and their hosts are suitable systems for the study of coevolution. This fascinating subject has interested both scientists and the common man for decades, but there are still many unanswered questions. One of the main puzzles is the apparent imperfect rejection behaviour against parasite eggs among hosts of brood parasites leading to a situation where many hosts experience severe costs of parasitism, which dramatically reduce their fitness. In order to lower these costs, hosts are expected to evolve counter-adaptations against parasitism. However, many host species show no rejection or only intermediate rejection rates against non-mimetic parasite eggs. In this review we consider several hypotheses set out to explain this phenomenon, and then we link these hypotheses with a consideration of various sources that can influence decision-making when hosts are faced with the possibility that a parasite egg is present in their nest.