In this article we review the present understanding of azimuthal and single spin asymmetries for inclusive and semi-inclusive particle production in unpolarized and polarized hadronic collisions at high energy and moderately large transverse momentum. After summarizing the experimental information available, we discuss and compare the main theoretical approaches formulated in the framework of perturbative QCD. We then present in some detail a generalization of the parton model with inclusion of spin and intrinsic transverse momentum effects. In this context, we extensively discuss the phenomenology of azimuthal and single spin asymmetries for several processes in different kinematical configurations. A comparison with the predictions of other approaches, when available, is also given. We finally emphasize some relevant open points and challenges for future theoretical and experimental investigation.