Blind and Visually impaired people (BVIP) face a range of practical difficulties when undertaking outdoor journeys as pedestrians. Over the past decade, a variety of assistive devices have been researched and developed to help BVIP navigate more safely and independently. In addition, research in overlapping domains are addressing the problem of automatic environment interpretation using computer vision and machine learning, particularly deep learning, approaches. Our aim in this article is to present a comprehensive review of research directly in, or relevant to, assistive outdoor navigation for BVIP. We breakdown the navigation area into a series of navigation phases and tasks. We then use this structure for our systematic review of research, analysing articles, methods, datasets and current limitations by task. We also provide an overview of commercial and non-commercial navigation applications targeted at BVIP. Our review contributes to the body of knowledge by providing a comprehensive, structured analysis of work in the domain, including the state of the art, and guidance on future directions. It will support both researchers and other stakeholders in the domain to establish an informed view of research progress.