Location awareness in wireless networks may enable many applications such as emergency services, autonomous driving and geographic routing. Although there are many available positioning techniques, none of them is adapted to work with massive multiple-in-multiple-out (MIMO) systems, which represent a leading 5G technology candidate. In this paper, we discuss possible solutions for positioning of mobile stations using a vector of signals at the base station, equipped with many antennas distributed over deployment area. Our main proposal is to use fingerprinting techniques based on a vector of received signal strengths. This kind of methods are able to work in highly-cluttered multipath environments, and require just one base station, in contrast to standard range-based and angle-based techniques. We also provide a solution for fingerprinting-based positioning based on Gaussian process regression, and discuss main applications and challenges.