Machine Learning (ML) approaches are increasingly being investigated as an alternative to Random Utility Models (RUMs) for modelling passenger mode choice. These approaches have the potential to provide valuable insights into choice modelling research questions. However, the research and the methodologies used are fragmented. Whilst systematic reviews on RUMs for mode choice prediction have long existed and the methods have been well scrutinised for mode choice prediction, the same is not true for ML models. To address this need, this paper conducts a systematic review of ML methodologies for modelling passenger mode choice. The review analyses the methodologies employed within each study to (a) establish the state-of-research frameworks for ML mode choice modelling and (b) identify and quantify the prevalence of methodological limitations in previous studies. A comprehensive search methodology across the three largest online publication databases is used to identify 468 unique records. These are screened for relevance, leaving 60 peer-reviewed articles containing 63 primary studies for data extraction. The studies are reviewed in detail to extract 15 attributes covering five research questions, concerning (i) classification techniques, (ii) datasets, (iii) performance estimation, (iv) hyper-parameter selection, and (v) model selection. The review identifies ten common methodological limitations. Five are determined to be methodological pitfalls, which are likely to introduce bias in the estimation of model performance. The remaining five are identified as areas for improvement, which may limit the achieved performance of the models considered. A further eight general limitations are identified, which highlight gaps in knowledge for future work.