The development of the platform economy has attracted the attention of geographers; in the last decade, publications have appeared that analyze certain aspects of this phenomenon. However, until recently there has been a lack of common understanding regarding the priorities and structure of the geographic research. Therefore, this study aims to summarize the available geographic research of the platform economy and to define the contours of future studies. The eight largest bibliographic databases have been searched using a special semantic search algorithm. More than 70 journal papers on the relevant topic have been found. A distribution of the papers by year and country is given. An analysis of the papers has shown that the existing diversity of the geographic research can be reduced to three maturing (comparative geographic, socio–geographic, and gravitational) and two germinating (spatial diffusion and constructive territorial) approaches. For each of these approaches, a list of the key problem areas is given, their solution defines the vectors of further research. Based on the existing publications and considering the capabilities of geographic research, it is argued that economic geographical, geosystemic, and regional approaches are also likely to appear in the future.