A small number of naturally occurring, proton-rich nuclides (the p-nuclei) cannot be made in the s- and r-processes. Their origin is not well understood. Massive stars can produce p-nuclei through photodisintegration of pre-existing intermediate and heavy nuclei. This so-called γ-process requires high stellar plasma temperatures and occurs mainly in explosive O/Ne burning during a core-collapse supernova. Although the γ-process in massive stars has been successful in producing a large range of p-nuclei, significant deficiencies remain. An increasing number of processes and sites has been studied in recent years in search of viable alternatives replacing or supplementing the massive star models. A large number of unstable nuclei, however, with only theoretically predicted reaction rates are included in the reaction network and thus the nuclear input may also bear considerable uncertainties. The current status of astrophysical models, nuclear input and observational constraints is reviewed. After an overview of currently discussed models, the focus is on the possibility to better constrain those models through different means. Meteoritic data not only provide the actual isotopic abundances of the p-nuclei but can also put constraints on the possible contribution of proton-rich nucleosynthesis. The main part of the review focuses on the nuclear uncertainties involved in the determination of the astrophysical reaction rates required for the extended reaction networks used in nucleosynthesis studies. Experimental approaches are discussed together with their necessary connection to theory, which is especially pronounced for reactions with intermediate and heavy nuclei in explosive nuclear burning, even close to stability.