Inferring the host of a virus given its genome is a challenging task, that has been addressed in the literature mainly through classifiers based on deep neural networks. Although powerful, these methods tend to overfit the data and to heavily exploit the similarity between the genomes in the training set and those in the test set, hindering the interpretation of the results in terms of viral adaptation to the host. I will show that simple maximum entropy models with a limited number of parameters can be used to determine the host of a virus given the viral genome with an accuracy comparable to deep neural networks, and that these models genuinely learn features that characterize the host-pathogen interaction. I will then discuss the implications of these results in terms of the adaptation of viruses to their hosts, focusing on what happens immediately after a host-shift event.