C*-algebras are norm closed and *-closed subalgebras of bounded linear operators on a Hilbert space. C*-algebras may come from topological dynamical systems, operator theory, non-commutative geometry as well as number theory. Classification of C*-algebras is a program to use  Elliott invariant, or K-theory related invariant to classify C*-algebras up to *-isomorphisms.  We will  try to give some description of current status of the program.