This work aims to cover the measurement, modeling, and analysis of waveform distortions in railway power systems. It is focused on waveform distortion as a phenomenon that includes harmonic distortion, interharmonic distortion, and supraharmonics. A comprehensive view of the interactions of waveform distortions in railway systems is needed, together with a grid perspective of power quality incorporating all aspects, sources, propagation, requirements, and effects. It is understood that the communities interested or involved in the subject of railway power systems would benefit from an integrated overview of the literature on the complex problem of waveform distortion. The literature review is divided into four categories: characterization and measurements, modeling, the application of artificial intelligence, and specific issues. For each category of work, the contributions are highlighted, and a discussion on opportunities, gaps, and critical observations is provided. The work successfully builds a framework for the subject with two main characteristics; the review is informative and propositional, providing a road map of opportunities for future works. Some aspects and recommendations can be highlighted. Suggestions for future works and research practices on waveform distortion in electrical transportation are offered.