This article describes research involving finite element simulations of women's pelvic floor, undertaken in the engineering schools of Lisbon and Oporto, in collaboration with the medical school of Oporto. These studies are motivated by the pelvic floor dysfunctions that lead namely to urinary incontinence and pelvic organ prolapse. This research ultimately aims at: (i) contributing to clarify the primary mechanism behind such disorders; (ii) providing tools to simulate the pelvic floor function and the effects of its dysfunctions; (iii) contributing to planning and performing surgeries in a more controlled and reliable way. The finite element meshes of the levator ani are based on a publicly available geometric data set, and use triangular thin shell or special brick elements. Muscle and soft tissues are assumed as (quasi-)incompressible hyperelastic materials. Skeletal muscles are transversely isotropic with a single fiber direction, embedded in an isotropic matrix. The fibers considered in this work may be purely passive, or active with input of neuronal excitation and consideration of the muscle activation process. The first assumption may be adequate to simulate passive deformations of the pelvic muscles and tissues (namely, under the extreme loading conditions of childbirth). The latter may be adequate to model faster contractions that occur in time intervals of the same order as those of muscle activation and deactivation (as in preventing urinary incontinence in coughing or sneezing). Numerical simulations are presented for the active deformation of the levator ani muscle under constant pressure and neural excitation, and for the deformation induced by a vaginal childbirth.