After decades of one-dimensional nucleosynthesis calculations, the growth of computational resources has meanwhile reached a level, which for the first time allows astrophysicists to consider performing routinely realistic multidimensional nucleosynthesis calculations in explosive and, to some extent, also in non-explosive environments. In the present contribution we attempt to give a short overview of the physical and numerical problems which are encountered in these simulations. In addition, we assess the accuracy that can be currently achieved in the computation of nucleosynthetic yields, using multidimensional simulations of core collapse supernovae as an example. ©2001 American Institute of Physics.