Authors:Shields et alAbstract:The prospects for the habitability of M-dwarf planets have long been debated, due to key differences between the unique stellar and planetary environments around these low-mass stars, as compared to hotter, more luminous Sun-like stars. Over the past decade, significant progress has been made by both space- and ground-based observatories to measure the likelihood of small planets to orbit in the habitable zones of M-dwarf stars. We now know that most M dwarfs are hosts to closely-packed planetary systems characterized by a paucity of Jupiter-mass planets and the presence of multiple rocky planets, with roughly a third of these rocky M-dwarf planets orbiting within the habitable zone, where they have the potential to support liquid water on their surfaces. Theoretical studies have also quantified the effect on climate and habitability of the interaction between the spectral energy distribution of M-dwarf stars and the atmospheres and surfaces of their planets. These and other recent results fill in knowledge gaps that existed at the time of the previous overview papers published nearly a decade ago by Tarter et al. (2007) and Scalo et al. (2007). In this review we provide a comprehensive picture of the current knowledge of M-dwarf planet occurrence and habitability based on work done in this area over the past decade, and summarize future directions planned in this quickly evolving field.