Analytical representations of potential energy hypersurfaces for the nuclear motion in polyatomic molecules from ab initio theory and experiment are discussed in a general way. The qualification of potential hypersurface representations from ab initio theory regarding the description of experimental data from rovibrational high-resolution spectroscopy and chemical reaction kinetics is analyzed in more detail for a restricted group of molecules including methane, CH 4 , ammonia, NH 3 , H 2 O 2 , and (HF) 2 . Current methods for the derivation of analytical representations of potential energy surfaces as well as some applications are reviewed.