  This paper reviews the moment graph technique that allows to translate
certain representation theoretic problems into geometric ones. For simplicity
we restrict ourselves to the case of semisimple complex Lie algebras. In
particular, we show how the original Kazhdan-Lusztig conjecture on the
characters of irreducible highest weight representations can be translated into
a multiplicity problem for parity sheaves on the (Langlands dual) flag variety.
