Optical current sensors have been developed and improved over the past few decades, and they have been increasingly employed in power systems, including smart and high-voltage grids. This is due to their many advantages over conventional electromagnetic current sensors, such as reduced size and weight, greater operational safety, and electromagnetic immunity. Like any measuring instrument or system, their quality and reliability are associated with measurement uncertainty, which quantifies their precision. This measurement uncertainty depends on a series of influencing quantities, such as the wavelength of light used in the sensor, the birefringence of the optical material used in the construction of the sensor, and environmental conditions, such as temperature and vibration. This article presents a review of the main influences that affect the quality and performance of optical current sensors and how these influences can be used to estimate measurement uncertainty. The main objective is to serve as a guide or reference for the identification and evaluation of uncertainty sources in optical current sensors used in power systems.