Healthcare systems are required to adopt specific approaches to address the complex challenges set by strict regulations and evolving user needs. In this article, we analyze and compare popular software development methodologies such as Agile, classical approaches (Waterfall, V-Model) and DevOps, based on results obtained from studies written in English and focusing solely on healthcare software development. The results obtained reveal that each methodology offers distinct advantages depending on the specific requirements and context of healthcare projects. In addition, the incorporation of emerging technologies such as artificial intelligence (AI) and blockchain significantly improves data management, real-time decision-making and security.