01
Calendar complications
Date is trivial. Day-date adds the weekday. Annual calendar knows months with 30 vs 31 days but needs adjusting once a year (March 1). Perpetual calendar accounts for leap years and is correct until 2100. Equation of time shows the difference between solar and clock time.
02
Timing complications
Chronograph = stopwatch. Flyback resets and restarts in one push. Rattrapante (split-seconds) times two events that start together. Tachymeter scales on the bezel convert elapsed time to speed.
03
Astronomical complications
Moonphase shows the lunar cycle (accurate ones drift by one day every 122 years). GMT/dual-time shows two timezones. World time shows all 24. Sidereal time tracks star position.
04
The mechanical showpieces
Tourbillon: the escapement spins in a rotating cage to average out gravity's effect. Minute repeater: chimes the time on demand via hammers and gongs — the holy grail of complications, often $500K+. Sonnerie: chimes automatically at every hour and quarter.