We consider fully coupled flow in deformable porous media, typically called poromechanics. The porous medium is assumed to be fully saturated. The mathematical model for poromechanics will be based on the quasi-static Biot equations. Fixed-stress splitting schemes will be first briefly presented for the linear Biot model. Convergence, stabilization and optimization of the schemes will be discussed. Further, a new family of splitting schemes based on approximate Schur complement will be discussed. Finally, a fixed-stress type splitting scheme for a relevant nonlinear poromechanics model will be presented (including convergence analysis).