Common methodologies used in software development include Agile, Scrum, Waterfall, and DevOps. Agile emphasizes iterative progress and flexibility, allowing teams to adapt to changes rapidly and deliver software in manageable increments. Scrum is a subset of Agile focusing on specific roles and ceremonies to manage the development process effectively. Waterfall follows a sequential model, where each phase must be completed before moving to the next, suitable for projects with well-defined requirements. DevOps bridges development and operations teams, promoting collaboration and continuous delivery. Together, these methodologies enhance efficiency and quality in software projects.