What development methodologies have you encountered?

Scrum, Kanban.

Scrum:

• Iterative and incremental development.
• Fixed sprints (2-4 weeks).
• Roles: Product Owner, Scrum Master, Development Team.
• Ceremonies: Daily Standup, Sprint Planning, Sprint Review, Sprint Retrospective.
• Artifacts: Product Backlog, Sprint Backlog, Increment.
• Flexibility and adaptability.

Kanban:

• Visualization of the workflow (Kanban board).
• Limiting work in progress (WIP limits).
• Focus on flow and continuous improvement.
• Metrics: Lead Time, Cycle Time.
• A more flexible approach to changing priorities than Scrum.