Multiple paternity is ubiquitous within the polyphyletic group called 'reptiles', especially within the lizards and snakes. Therefore, the probability of sperm competition occurring, and being intense, is high. Squamates exhibit a diversity of tactics to ensure fertilization success in the face of sperm competition. The duration of female sperm storage, which can be many months and even years in some species, remains an enigma. Here, we emphasize some mechanisms that might affect patterns of paternity, the source and function of ejaculates and features of the female reproductive tract that may aid in long-term sperm storage. In doing so, we present a new analysis of the relationship between sperm size, the strength of sperm competition and the duration of female sperm storage. Lizards and snakes are a diverse group that has provided many excellent models for the study of an array of life-history strategies. However, when it comes to postcopulatory sexual selection, there is much left to discover. This article is part of the theme issue 'Fifty years of sperm competition'.