  We survey crystalline cohomology, crystals, and formal group laws with an
emphasis on geometry. We apply these concepts to K3 surfaces, and especially to
supersingular K3 surfaces. In particular, we discuss stratifications of the
moduli space of polarized K3 surfaces in positive characteristic, Ogus'
crystalline Torelli theorem for supersingular K3 surfaces, the Tate conjecture,
and the unirationality of K3 surfaces.
