Remote sensing of plant phenology as an indicator of climate change and for mapping land cover has received significant scientific interest in the past two decades. The advancing of spring events, the lengthening of the growing season, the shifting of tree lines, the decreasing sensitivity to warming and the uniformity of spring across elevations are a few of the important indicators of trends in phenology. The Sentinel-2 satellite sensors launched in June 2015 (A) and March 2017 (B), with their high temporal frequency and spatial resolution for improved land mapping missions, have contributed significantly to knowledge on vegetation over the last three years. However, despite the additional red-edge and short wave infra-red (SWIR) bands available on the Sentinel-2 multispectral instruments, with improved vegetation species detection capabilities, there has been very little research on their efficacy to track vegetation cover and its phenology. For example, out of approximately every four papers that analyse normalised difference vegetation index (NDVI) or enhanced vegetation index (EVI) derived from Sentinel-2 imagery, only one mentions either SWIR or the red-edge bands. Despite the short duration that the Sentinel-2 platforms have been operational, they have proved their potential in a wide range of phenological studies of crops, forests, natural grasslands, and other vegetated areas, and in particular through fusion of the data with those from other sensors, e.g., Sentinel-1, Landsat and MODIS. This review paper discusses the current state of vegetation phenology studies based on the first five years of Sentinel-2, their advantages, limitations, and the scope for future developments.