Waterfall (1970)
The textbook sequential model: requirements → design → implementation → verification → maintenance. Each phase ends before the next begins. Famously presented in Royce's 1970 paper — as an example of how NOT to do it. The diagram got extracted, the warning got lost, and an entire industry was built on a misread paper.
↳ when waterfall actually works
Iterative & Incremental
Build a thin slice, learn from it, build the next slice. Larman & Basili (2003) traced iterative development back to NASA's Mercury project (1959) — well before Agile was a word. Iterative accepts that you don't know everything up front and structures the project to surface what you don't know early, when changes are still cheap.
Spiral (Boehm, 1986)
Risk-driven iteration. Each spiral has four quadrants: identify objectives, analyze risk, develop & test, plan the next spiral. The size of each spiral is proportional to risk — high-risk projects start small and ramp up. Most useful on large, expensive efforts where prematurely committing is catastrophic (defense, aerospace).
Agile (2001 → present)
Less a single methodology than a family of practices anchored on the Agile Manifesto's four values: individuals over processes, working software over docs, customer collaboration over contract negotiation, responding to change over following a plan. The most common implementations are Scrum (time-boxed sprints, fixed roles) and Kanban (continuous flow with WIP limits). Track 03 covers both.
Hybrid
What most large orgs actually run. The contract / governance layer is waterfall (fixed scope, fixed budget, board reviews); the execution layer is agile (sprints, demos, iterative refinement). PMBOK 7 explicitly accommodates hybrid — it's no longer the embarrassing compromise it was a decade ago.