Inverse functional equations are studied for the partition functions and for the correlation functions of various models. The validity of the inverse relation for the partition function is justified with the help of approximations by quasi-one-dimensional models defined on strips of increasing size. The possibility of determining the partition function through the use of the inverse and other symmetry relations, coupled to analyticity hypotheses, is briefly investigated on the two-dimensional Ising model, with a field. The group generated by the inverse relation and the spatial symmetries of the model is studied in a three-dimensional case. Inverse relations are also exhibited, firstly for two-point and then for n-point correlation functions. They are first put into evidence by a geometric approach and then verified on a particular high-temperature expansion.