The extensive and sometimes unregulated use of synthetic chemicals, such as drugs, preservatives, and pesticides, is posing big threats to global health, the environment, and food security. This has stimulated the research of new strategies to deal with bacterial infections in animals and humans and to eradicate pests. Plant extracts, particularly essential oils, have recently emerged as valid alternatives to synthetic drugs, due to their properties which include antibacterial, antifungal, anti-inflammatory, antioxidant, and insecticidal activity. This review discusses the current research on the use of electrospinning to encapsulate essential oils into polymeric nanofibres and achieve controlled release of these bioactive compounds, while protecting them from degradation. The works here analysed demonstrate that the electrospinning process is an effective strategy to preserve the properties of essential oils and create bioactive membranes for biomedical, pharmaceutical, and food packaging applications.