I will discuss three questions in this talk. (Existence) Given a smooth hypersurface Y of a projective manifold X with numerically trivial normal bundle, does there exist a codimension one foliation on X having Y as a compact leaf? (Abelian holonomy) What can we say about foliations having a compact leaf with abelian holonomy? (Factorization) It is rather easy to construct foliations on projective surfaces having compact leaves with non-solvable holonomy. In higher dimensions, the only known examples are pull-backs of foliations on surfaces through rational morphism. Is this a general phenomenon? In particular, does the holonomy of compact leaves factor through curves when non solvable? (Joint work with B.Claudon, F. Loray, F. Touzet)