We survey a variety of experimental paradigms for studying animal abilities to count, to understand numerical information and to perform simple arithmetic operations. There is a huge body of evidence that different forms and elements of quantitative judgement and numerical competence are spread across a wide range of species, both vertebrate and invertebrate. Here we pay particular attention to the display of numerical competence in ants. The reason is that most of the existing experimental schemes for studying numerical processing in animals, although often elegant, are restricted by studying subjects at the individual level, or by the use of artificial communicative systems. In contrast, the information-theoretic approach that was elaborated for studying number-related skills in ants employs their own communicative means and, thus, does not require the subjects to solve any artificial learning problems, such as learning intermediary languages, or even learning to solve multiple choice problems. Using this approach, it was discovered that members of highly social ant species possessed numerical competence. They were shown to be able to pass information about numbers and to perform simple arithmetic operations with small numbers. We suggest that applying ideas of information theory and using the natural communication systems of highly social animals can open new horizons in studying numerical cognition.