In recent decades, several assistive technologies for visually impaired and blind (VIB) people have been developed to improve their ability to navigate independently and safely. At the same time, simultaneous localization and mapping (SLAM) techniques have become sufficiently robust and efficient to be adopted in the development of assistive technologies. In this paper, we first report the results of an anonymous survey conducted with VIB people to understand their experience and needs; we focus on digital assistive technologies that help them with indoor and outdoor navigation. Then, we present a literature review of assistive technologies based on SLAM. We discuss proposed approaches and indicate their pros and cons. We conclude by presenting future opportunities and challenges in this domain.