The session-based recommendation (SBR) garners increasing attention due to its ability to predict anonymous user intents within limited interactions. Emerging efforts incorporate various kinds of side information into their methods for enhancing task performance. In this survey, we thoroughly review the side information-driven session-based recommendation from a data-centric perspective. Our survey commences with an illustration of the motivation and necessity behind this research topic. This is followed by a detailed exploration of various benchmarks rich in side information, pivotal for advancing research in this field. Moreover, we delve into how these diverse types of side information enhance SBR, underscoring their characteristics and utility. A systematic review of research progress is then presented, offering an analysis of the most recent and representative developments within this topic. Finally, we present the future prospects of this vibrant topic.