In this paper we use filtered Lyapunov functions, introduced in previous works, to construct a general framework for the global stabilization of nonlinear systems. Filtered Lyapunov functions are Lyapunov functions which may depend on parameters satisfying differential equations. The main feature of filtered Lyapunov functions is that it is easy to construct and combine them even for nontriangular systems to obtain composite filtered Lyapunov functions which may be used for Lyapunov-based design of stabilizing controllers. Tools for the design of composite filtered Lyapunov functions are given and used to prove new global stabilization results via dynamic feedback.