Understanding complications.
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At its most basic, a watch's movement tracks the passage of hours, minutes, and seconds. The most impressive watches, though, include complications. There are the standards – your date display and chronograph (stopwatch function), and so forth. And then there are these three, each a triumph of engineering, with complexity that elicits lust and awe in those who know watches.

Minute Repeater
Prior to the 17th century, once the sun went down and the candles were snuffed, telling time became guesswork. Then pocket watches with minute repeaters appeared, their movements integrating tiny hammers and gongs that sounded different tones for the hour, quarter-hour, and minutes to ring in the exact time. They fell out of favor when matches were invented in the 19th century.

Perpetual Calendar
This is the Will Hunting of mechanical calendars, able to account for the differing lengths of months, and even leap years, too. As a result, most perpetual calendar watches display not only the date and month, but also the day of the week, the year, and the moon phase. The movement needs to be set only three times every 400 years – or once in your lifetime at most, if you're lucky enough to own one.

Tourbillon
By housing the balance wheel and escapement in a rotating cage, this incredibly intricate complication compensates for the negative interference of gravity on a mechanical movement. Invented in 1795 by Breguet, it was implemented sparingly through the 1940s, then became popular starting in the mid-'80s as luxury watchmakers sought to show off their mastery.