The power system is transitioning from the traditional one-way system to a more integrated and complex system with more active end-users and with generation and reverse power flow at the distribution level. As a part of this transition, flexible resources such as energy storage systems, electrical vehicles and demand response are increasingly being deployed in distribution systems. Among their benefits, flexibility services are often directly or indirectly associated with a positive impact on the security of electricity supply (SoS). However, the SoS perspective is not given satisfactory attention in the existing research literature. The objective of this article is therefore to provide a structured review of methodologies for assessing the impact of flexible resources in distribution systems on SoS. Four main aspects of security of electricity supply are distinguished in this article: energy availability, power capacity, reliability of supply, and power quality. Flexibility services are classified in relation to each of these aspects, and the literature is reviewed for methods and indicators for quantifying their impact. Finally, the article discusses the need for more holistic and comprehensive assessments of SoS considering flexible resources and possible implications for managing the SoS of the power system in the future.