  For any finitely generated abelian group $Q$, we reduce the problem of
classification of $Q$-graded simple Lie algebras over an algebraically closed
field of "good" characteristic to the problem of classification of gradings on
simple Lie algebras. In particular, we obtain the full classification of
finite-dimensional $Q$-graded simple Lie algebras over any algebraically closed
field of characteristic $0$ based on the recent classification of gradings on
finite dimensional simple Lie algebras.
  We also reduce classification of simple graded modules over any $Q$-graded
Lie algebra (not necessarily simple) to classification of gradings on simple
modules. For finite-dimensional $Q$-graded semisimple algebras we obtain a
graded analogue of the Weyl Theorem.
