This paper presents an overview of both T-Trefftz and F-Trefftz finite element methods (FEM) and its application in various engineering problems. Recent developments on the T-Trefftz finite element formulation of nonlinear problems of minimal surface, F-Trefftz methods for composite, skin tissue, and functionally graded materials are described. Formulations for all cases are derived by means of a modified variational functional and T-complete solutions or fundamental solutions. Generation of elemental stiffness equations from the modified variational principle is also discussed. Finally, a brief summary of the approach is provided and future trends in this field are identified.