Over the last 40–50 years, ethology has become increasingly quantitative and computational. However, when analysing animal behavioural sequences, researchers often need help finding an adequate model to assess certain characteristics of these sequences while using a relatively small number of parameters. In this review, I demonstrate that the information theory approaches based on Shannon entropy and Kolmogorov complexity can furnish effective tools to analyse and compare animal natural behaviours. In addition to a comparative analysis of stereotypic behavioural sequences, information theory can provide ideas for particular experiments on sophisticated animal communications. In particular, it has made it possible to discover the existence of a developed symbolic “language” in leader-scouting ant species based on the ability of these ants to transfer abstract information about remote events.