This paper discusses contemporary problems concerning ship microgrids. It focuses on the role of power electronics and power quality issues, both conventional, such as voltage and frequency variations, and new issues, such as waveform distortions ensuing from the wide proliferation of power electronics in ship microgrids. The paper also contains a discussion on the provisions of the Unified Requirements of International Association of Classification Societies and other leading power quality standards in the industry, with an emphasis on Total Harmonic Distortion (THD) definition. An overview of power converters for high power applications in ships and their impact on ship networks is also given. Next, original results of various power quality phenomena recorded in ship microgrids are presented and commented on, followed by a review and recommendations for maritime microgrid modeling and signal processing methods for power quality assessment in the discussed systems. Finally, preliminary proposals for power quality control are presented.