Extended system path integral molecular dynamics algorithms have been developed that can generate efficiently averages in the quantum mechanical canonical ensemble [M. E. Tuckerman, B. J. Berne, G. J. Martyna, and M. L. Klein, J. Chem. Phys. 99, 2796 (1993)]. Here, the corresponding extended system path integral molecular dynamics algorithms appropriate to the quantum mechanical isothermal-isobaric ensembles with isotropic-only and full system cell fluctuations are presented. The former ensemble is employed to study fluid systems which do not support shear modes while the latter is employed to study solid systems. The algorithms are constructed by deriving appropriate dynamical equations of motions and developing reversible multiple time step algorithms to integrate the equations numerically. Effective parallelization schemes for distributed memory computers are presented. The new numerical methods are tested on model (a particle in a periodic potential) and realistic (liquid and solid para-hydrogen and liquid butane) systems. In addition, the methodology is extended to treat the path integral centroid dynamics scheme, [J. Cao and G. A. Voth, J. Chem. Phys. 99, 10070 (1993)], a novel method which is capable of generating semiclassical approximations to quantum mechanical time correlation functions.