What is the difference between Agile and Waterfall methodologies?

Waterfall is a sequential, linear approach where each phase must complete before the next begins - good for stable requirements but inflexible to change. Agile is iterative, delivering working software in short cycles (sprints), embracing changing requirements, and emphasizing collaboration. Waterfall: extensive documentation, big upfront design. Agile: continuous delivery, adaptability, customer feedback. Most modern software development uses Agile or hybrid approaches.