The specific mechanism and astrophysical site for the production of half of the heavy elements, the so-called r-nuclei, remains to be found. We address the problem making improvements along two main fronts: the astrophysical environment and the properties of the nuclei far from stability. Observational data indicate that there are two components. The heavy r-process nuclei (A>130) are produced by rapid neutron capture in a yet unknown site. The other component corresponds to the "lighter heavy nuclei" or weak r-process. These nuclei are produced by charge-particle reactions (CPR) and neutron captures in what it was also known as light element primary process (LEPP). Our nucleosynthesis studies are based on trajectories of hydrodynamical simulations for core-collapse supernovae and their subsequent neutrino-driven winds. We show that LEPP elements can be produced in neutrino-driven winds and we relate their abundances to the neutrino emission from the nascent neutron star. Based on the latest hydrodynamical simulations, heavy r-process elements cannot be synthesized in the neutrino-driven winds. However, by artificially increasing the wind entropy, elements up to A=195 can be made. In this way one can mimic the general behavior of an ejecta where the r-process occurs. We use this approach to study the impact of the nuclear physics input (nuclear masses, neutron capture cross sections, and beta-delayed neutron emission) and of the long-time dynamical evolution on the final abundances.