Plasma-based electrosurgical devices have long been employed for tissue coagulation, cutting, desiccation, and cauterizing. Despite their clinical benefits, these technologies involve tissue heating and their effects are primarily heat-mediated. Recently, there have been significant developments in cold atmospheric pressure plasma (CAP) science and engineering. New sources of CAP with well-controlled temperatures below 40 °C have been designed, permitting safe plasma application on animal and human bodies. In the last decade, a new innovative field, often referred to as plasma medicine, which combines plasma physics, life science, and clinical medicine has emerged. This field aims to exploit effects of mild plasma by controlling the interactions between plasma components (and other secondary species that can be formed from these components) with specific structural elements and functionalities of living cells. Recent studies showed that CAP can exert beneficial effects when applied selectively in certain pathologies with minimal toxicity to normal tissues. The rapid increase in new investigations and development of various devices for CAP application suggest early adoption of cold plasma as a new tool in the biomedical field. This review explores the latest major achievements in the field, focusing on the biological effects, mechanisms of action, and clinical evidence of CAP applications in areas such as skin disinfection, tissue regeneration, chronic wounds, and cancer treatment. This information may serve as a foundation for the design of future clinical trials to assess the efficacy and safety of CAP as an adjuvant therapy for skin cancer.