Agile software development is a methodology focused on incremental development through continual planning and collaboration, emphasizing customer satisfaction, flexibility, and adaptability. Key agile methods include Scrum, Extreme Programming (XP), and Dynamic Systems Development Method (DSDM), each with distinct processes and benefits. While agile promotes rapid delivery and responsiveness to change, it can suffer from challenges related to insufficient documentation and the potential for misinterpretation among team members.