Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We study the homological finiteness properties FPm of wreath products Gamma = H X-integral G. We show that, when H has infinite abelianization, Gamma is of type FPm if and only if both G and H have type FPm and G acts ( diagonally) on X-i with stabilizers of type FPm-i and with finitely many orbits for all 1 <= i <= m. If furthermore H is torsion-free, we give a criterion for Gamma to be Bredon-FPm with respect to the class of finite subgroups of Gamma. Finally, when H has infinite abelianization and chi : Gamma . R is a non-zero homomorphism with chi( H) = 0, we classify when [chi] belongs to the Bieri-Neumann-Strebel-Renz invariant Sigma(m)( Gamma, Z).662 437457Brazilian-French Network in MathematicsConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)