let x be a projective smooth variety over an algebraically closed field k. if k has characteristic zero, then the singular (betti) cohomology groups of x are finitely generated abelian groups and therefore all the invariants associated to them are discrete and in fact do not change under good deformations. if k has positive characteristic, then the crystalline cohomology groups of x have a much richer structure and are called f-crystals over k. in particular, one can associate to them many subtle invariants which vary a lot under good deformations and which could be of either discrete or continuous nature. we present an accessible survey of the classification of f-crystals over k via subtle invariants with an emphasis on the recent results obtain by us, by gabber and us, and by lau, nicole, and us.