Agile and waterfall methodologies represent distinct approaches to software development, each with its advantages and suitability for different project requirements. Agile emphasizes iterative development, collaboration, and flexibility, making it ideal for dynamic projects with evolving requirements. Scrum, Kanban, and Extreme Programming (XP) are popular agile frameworks that prioritize customer feedback and incremental delivery. Waterfall follows a sequential, phase-based model, suitable for projects with well-defined specifications and minimal changes. Choosing the right methodology depends on factors such as project complexity, team dynamics, and stakeholder expectations.