Accurately modelling crashes, and predicting crash occurrence and associated severities are a prerequisite for devising countermeasures and developing effective road safety management strategies. To this end, crash prediction modelling using machine learning has evolved over two decades. With the advent of big data that provides unprecedented opportunities to better understand the crash mechanism and its determinants, such efforts will likely be accelerated. To gear these efforts, understanding state-of-the-art machine learning-based crash prediction models becomes paramount to summarise the lessons learned from past efforts, which can assist in developing robust and accurate models. This review paper aims to address this gap by systematically reviewing the machine learning studies on crash modelling. Models are reviewed from three aspects of the application: (a) crash occurrence (or real-time crash) prediction, (b) crash frequency prediction, and (c) injury severity prediction. Further, model intricacies that impact model performance are identified and thoroughly reviewed. This comprehensive review highlights specific gaps and future research needs in three aforementioned model applications, such as improper selection of non-crash events for crash occurrence models, the inability of future forecasting of crash frequency models, and inconsistency in injury severity classes. Critical research needs relating to model development, evaluation, and application are also discussed. This review envisages methodological advancements in machine learning models for crash prediction modelling and leveraging big data to better link crashes with its determinants.