How do TVS diodes work?
In theory (in the land of spherical cows), TVS diodes are the same as other Zener diodes.

In practice, Semtech says:


  The electrical characteristics of the transient protection circuit are determined by factors such as junction area, doping concentration, and substrate resistivity. The surge power and surge current capability of the TVS diode are proportional to the junction area. TVS diodes are constructed with large cross sectional area junctions for absorbing high transient current. While the VI characteristic curve of the TVS diode is similar to that of a zener diode, TVS diodes are specifically designed, characterized, and tested for transient voltage suppression. By contrast, zener diodes are designed and specified for voltage regulation.


In other words, normal Zener diodes are designed for a small current (i.e., with a small junction area), which flows continuously. The larger junction in TVS diodes can endure much larger breakdown currents, but only for a short time.

Furthermore, normal Zener diodes are designed to get an accurate breakdown voltage at a specific current. TVS diodes have somewhat looser tolerances, but this does not matter because they have to handle wildly varying currents, and the voltage varies with current anyway. (This is not as much a difference in construction but in testing.)

Bidirectional TVS diodes are constructed as two diodes connected back-to-back (often on the same die). Such a construction would not make sense for voltage-regulating Zener diodes.