Since Feynman path integrals give a new definition of quantum dynamics, it is interesting to apply them, even on a heuristic level, to domains where the usual approaches to quantization meet difficulties, for instance general relativity. In particular a definition of Feynman path integrals on curved spaces is needed. C. De Witt discusses the possibility of such a definition in analogy with the work done for the Wiener integrals on manifolds. Another domain where both the usual and the Feynman quantization procedures meet difficulties is afforded by Lagrangians involving higher than quadratic terms in the velocities.