Ship microgrids have recently received increased attention, mainly due to the extensive use of power electronically interfaced loads and sources. Characteristics of these microgrids are similar to islanded terrestrial microgrids, except the presence of highly dynamic large loads, such as propulsion loads. The presence of such loads and sources with power-electronic converter interfaces lead to severe power quality issues in ship microgrids. Generally, these issues can be classified as voltage variations, frequency variations and waveform distortions which are commonly referred to as harmonic distortions. Amongst the solutions identified, energy storage is considered to be the most promising technology for mitigating voltage and/or frequency deviations. Passive filtering is the commonly used technology for reducing harmonic distortions, which requires bulky capacitors and inductors. Active filtering is emerging as an alternative, which could be realised even within the same interfacing converter of the energy storage system. The aim of this paper is to investigate recent developments in these areas and provide readers with a critical review on power quality issues, energy storage technologies and strategies that could be used to improve the power quality in ship microgrids. Moreover, a brief introduction to ship power system architectures is also presented in the paper.