© Springer International Publishing AG 2017. A k-nearest neighbor (kNN) query determines the k nearest points, using distance metrics, from a given location. An all k-nearest neighbor (AkNN) query constitutes a variation of a kNN query and retrieves the k nearest points for each point inside a database. Their main usage resonates in spatial databases and they consist the backbone of many location-based applications and not only. Although (A)kNN is a fundamental query type, it is computationally very expensive. During the last years a multiplicity of research papers has focused around the distributed (A)kNN query processing on the cloud. This work constitutes a survey of research efforts towards this direction. The main contribution of this work is an up-to-date review of the latest (A)kNN query processing approaches. Finally, we discuss various research challenges and directions of further research around this domain.