Future communication systems are faced with increased demand for high capacity, dynamic bandwidth, reliability and heterogeneous traffic. To meet these requirements, networks have become more complex and thus require new design methods and monitoring techniques, as they evolve towards becoming autonomous. Machine learning has come to the forefront in recent years as a promising technology to aid in this evolution. Optical fiber communications can already provide the high capacity required for most applications, however, there is a need for increased scalability and adaptability to changing user demands and link conditions. Accurate performance monitoring is an integral part of this transformation. In this paper we review optical performance monitoring techniques where machine learning algorithms have been applied. Moreover, since alot of OPM depends on knowledge of the signal type, we also review work for modulation format recognition and bitrate identification. We additionally briefly introduce a neuromorphic approach to OPM as an emerging technique that has only recently been applied to this domain.