The programming methodology that focuses on incremental development is known as Agile. Agile emphasizes flexibility, collaboration, and iterative progress, allowing software to evolve through smaller, manageable increments called sprints. Each iteration involves planning, development, testing, and evaluation, promoting continuous improvement. Agile enables teams to adapt to changing requirements more effectively than traditional methods, which often follow a linear approach. This iterative process fosters team collaboration and allows for quick responses to user feedback, leading to higher quality products.