The Waterfall methodology is a linear, sequential approach to product development that divides the process into distinct phases, including requirements gathering, design, development, testing, deployment, and maintenance. It is well-suited for projects with well-defined requirements and a clear understanding of the end goal, but can be inflexible and does not allow for changes once development has started. In contrast, Agile methodology emphasizes collaboration and adaptation, dividing the product development process into short iterations called sprints, which allows for quick adaptation to changing requirements and feedback from users. Lean methodology focuses on delivering customer value and speed to market, emphasizing the rapid development and delivery of a minimum viable product (MVP). Each methodology has its strengths and weaknesses, and the best approach depends on the specific needs and constraints of the project. It is also important not to become too dogmatic about methodologies, as each team's unique problem may require a different approach.