Point clouds are becoming essential in key applications with advances in capture technologies leading to large volumes of data. Compression is thus essential for storage and transmission. In this work, the state of the art for geometry and attribute compression methods with a focus on deep learning based approaches is reviewed. The challenges faced when compressing geometry and attributes are considered, with an analysis of the current approaches to address them, their limitations and the relations between deep learning and traditional ones. Current open questions in point cloud compression, existing solutions and perspectives are identified and discussed. Finally, the link between existing point cloud compression research and research problems to relevant areas of adjacent fields, such as rendering in computer graphics, mesh compression and point cloud quality assessment, is highlighted.