Here we give a brief survey on recent mathematical works concerning the Faddeev and Skyrme models.One of the most facinating phenomena descibed by these models are the knoted topological soliton solutions which are fundamentally different from many other well-known feild theory models such as instantons and monopoles in the Yang-Mills or the general gauge field theory,bubbles in the nonlinear sigma models or ferromagnetisms and vortices in superconductors and superfluids.In this lecture we shall illustrate some key features of these models that lead to the exisitence of stable knoted solitons and to discuss some possible implications in other problems.