Background Natural disasters and epidemics can strain already‐fragile health systems, diverting resources away from essential sexual and reproductive health (SRH) services, threatening supply chains, and adversely impacting access to health facilities. Objective To describe how natural disasters and epidemics affect multiple dimensions of SRH service delivery and outcomes, and identify potential approaches to facilitate resumption of services. Search strategy Key words searched in Google Scholar, PubMed, and Scopus. Selection criteria Studies published in English between 2005 and 2020 covering events in low‐ and middle‐income countries. Data collection and analysis This review was developed and reported according to the Preferred Reporting Items for Systematic Reviews and Meta‐analyses (PRISMA) 2009 checklist. The initial electronic database searching yielded 64 345 studies, but after screening 13 studies were included in the final review. Main results Across contexts, disruptive events worsened the availability of and women's access to SRH services, contributed to decreased utilization of SRH services, and often resulted in lower use of family planning, particularly methods requiring facility‐based interaction. Conclusion SRH in disaster response plans must be prioritized, as women often lose access to these essential services at a time when they are at their most vulnerable. Evidence regarding effective interventions and policies is lacking.