The main idea of the method of differential constraints is very simple: to define suitable constraint(s) for a given partial differential equations (PDE) in such a way that the over determined system obtained will be compatible and can be solved using the existing methods. Several methods were developed, which use the correctly-specified differential constraints in order to find exact solutions for some classes of nonlinear PDEs. Notwithstanding its efficiency was demonstrated on PDEs and systems involving only quadratic nonlinearities, the method can be adopted also for solving nonlinear equations with a more complicated structure. The constructive method was generalized on systems of PDEs and several nonlinear systems arising in various applications were examined in order to construct exact solutions. The systems of ordinary differential equations obtained were enabling the statisticians to construct multiparametric families of exact solutions of the nonlinear equation.