Modern society is highly dependent on a reliable electricity supply. During explosive volcanic eruptions, tephra contamination of power networks (systems) can compromise the reliability of supply. Outages can have significant cascading impacts for other critical infrastructure sectors and for society as a whole. This paper summarises known impacts to power systems following tephra falls since 1980. The main impacts are (1) supply outages from insulator flashover caused by tephra contamination, (2) disruption of generation facilities, (3) controlled outages during tephra cleaning, (4) abrasion and corrosion of exposed equipment and (5) line (conductor) breakage due to tephra loading. Of these impacts, insulator flashover is the most common disruption. The review highlights multiple instances of electric power systems exhibiting tolerance to tephra falls, suggesting that failure thresholds exist and should be identified to avoid future unplanned interruptions. To address this need, we have produced a fragility function that quantifies the likelihood of insulator flashover at different thicknesses of tephra. Finally, based on our review of case studies, potential mitigation strategies are summarised. Specifically, avoiding tephra-induced insulator flashover by cleaning key facilities such as generation sites and transmission and distribution substations is of critical importance in maintaining the integrity of an electric power system.