  We investigate the collapsing geometry of hyperk\"ahler 4-manifolds. As
applications we prove two well-known conjectures in the field.
  (1) Any collapsed limit of unit-diameter hyperk\"ahler metrics on the K3
manifold is isometric to one of the following: the quotient of a flat 3-torus
by an involution, a singular special K\"ahler metric on the 2-sphere, or the
unit interval.
  (2) Any complete hyperk\"ahler 4-manifold with finite energy (i.e.,
gravitational instanton) is asymptotic to a model end at infinity.
