Machine learning (ML) pervades an increasing number of academic disciplines and industries. Its impact is profound, and several fields have been fundamentally altered by it, autonomy and computer vision for example; reliability engineering and safety will undoubtedly follow suit. There is already a large but fragmented literature on ML for reliability and safety applications, and it can be overwhelming to navigate and integrate into a coherent whole. In this work, we facilitate this task by providing a synthesis of, and a roadmap to this ever-expanding analytical landscape and highlighting its major landmarks and pathways. We first provide an overview of the different ML categories and sub-categories or tasks, and we note several of the corresponding models and algorithms. We then look back and review the use of ML in reliability and safety applications. We examine several publications in each category/sub-category, and we include a short discussion on the use of Deep Learning to highlight its growing popularity and distinctive advantages. Finally, we look ahead and outline several promising future opportunities for leveraging ML in service of advancing reliability and safety considerations. Overall, we argue that ML is capable of providing novel insights and opportunities to solve important challenges in reliability and safety applications. It is also capable of teasing out more accurate insights from accident datasets than with traditional analysis tools, and this in turn can lead to better informed decision-making and more effective accident prevention.