Antimicrobial resistance is a global health problem that demands all possible means to control it. Mathematical modelling is a valuable tool for understanding the mechanisms of AMR development and spread, and can help us to investigate and propose novel control strategies. However, it is of vital importance that mathematical models have a broad utility, which can be assured if good modelling practice is followed. The objective of this study was to provide a comprehensive systematic review of published models of AMR development and spread. Furthermore, the study aimed to identify gaps in the knowledge required to develop useful models. The review comprised a comprehensive literature search with 38 selected studies. Information was extracted from the selected papers using an adaptation of previously published frameworks, and was evaluated using the TRACE good modelling practice guidelines. None of the selected papers fulfilled the TRACE guidelines. We recommend that future mathematical models should: a) model the biological processes mechanistically, b) incorporate uncertainty and variability in the system using stochastic modelling, c) include a sensitivity analysis and model external and internal validation. Many mathematical models of AMR development and spread exist. There is still a lack of knowledge about antimicrobial resistance, which restricts the development of useful mathematical models.