In the last decade, temporal networks and static and temporal hypergraphs have enabled modelling connectivity and spreading processes in a wide array of real-world complex systems such as economic transactions, information spreading, brain activity and disease spreading. In this manuscript, we present the Reticula C++ library and Python package: A comprehensive suite of tools for working with real-world and synthetic static and temporal networks and hypergraphs. This includes various methods of creating synthetic networks and randomised null models based on real-world data, calculating reachability and simulating compartmental models on networks. The library is designed principally on an extensible, cache-friendly representation of networks, with an aim of easing multi-thread use in the high-performance computing environment.