Multiscale modelling of drug mechanism and safety

•We introduce models at molecular, cellular and omics, and organ and system levels.•Models share mathematics as the language and informatics as a tool to study biology.•Integration of models at different scales brings insights and increases productivity.•It is high time to understand drug mechanism and safety with multiscale modelling. Here, we introduce models at three levels—molecular level, cellular and omics level, and organ and system level—that study drug mechanism and safety in preclinical drug discovery. The models differ in both their scope of study and technical details, but are all rooted in mathematical descriptions of complex biological systems, and all require informatics tools that handle large-volume, heterogeneous, and noisy data. We present principles and recent developments with examples at each level and highlight the synergy by a case study. We proffer a multiscale modelling view of drug discovery, call for a seamless flow of information in the form of models, and examine potential impacts. It is high time to integrate computational models at multiple levels to understand drug mechanism and safety.