Part 1 Overview: Motivation, definition, and history of HCCI/CAI engines. Part 2 Gasoline HCCI/CAI combustion engines: Overview of CAI/HCCI gasoline engines; Two-stroke CAI engines; Four-stroke gasoline HCCI engines with thermal management; Four-stroke CAI engines with residual gas trapping; Four-stroke CAI engines with internal exhaust gas recirculation (EGR); HCCI control; CAI control and CAI/SI switching; Fuel effects in CAI gasoline engines. Part 3 Diesel HCCI combustion engines: Overview of HCCI diesel engines; HCCI combustion with early and multiple injection in the heavy-duty diesel engine; Narrow angle direct injection (NADITM) concept for HCCI diesel combustion; Low-temperature and premixed combustion concept with late injection; HCCI fuel requirements. Part 4 HCCI/CAI combustion engines with alternative fuels: Natural gas HCCI engines; HCCI engines with other fuels. Part 5 Advances modeling and experimental techniques: Auto-ignition and chemical kinetic mechanisms of HCCI combustion; Overview of modeling techniques and their application to HCCI/CAI engines; Overview of advanced optical techniques and their applications to HCCI/CAI engines. Part 6 Future directions for CAI/HCCI engines: Outlook and future directions in HCCI/CAI engines.