The programming methodology that focuses on iterative development and user feedback is known as Agile. This approach promotes collaboration among cross-functional teams, allowing for continuous improvement throughout the development cycle. Agile methodologies prioritize delivering functional software in shorter iterations, enabling teams to gather feedback early and often. By adapting based on user input, Agile ensures that the final product aligns closely with customer needs. This flexibility enhances product quality and responsiveness to market changes, making Agile a popular choice for modern software development.