  Lichnerowicz-Jacobi cohomology and homology of Jacobi manifolds are reviewed.
We present both in a unified approach using the representation of the Lie
algebra of functions on itself by means of the hamiltonian vector fields. The
use of the associated Lie algebroid allows to prove that the
Lichnerowicz-Jacobi cohomology and homology are invariant under conformal
changes of the Jacobi structure and to stablish the duality between
Lichnerowicz-Jacobi cohomology and homology when the modular class vanishes. We
also compute the Lichnerowicz-Jacobi cohomology and homology for a large
variety of examples.
