This paper reviews the principles

problems and new progresses of the finite element method for microwave and optical waveguide devices.It discusses the significance of the variational formulae suitable for different problems

concentrates on the techniques to avoid or eliminate spurious modes and to deal with open-boundary problems.It also comments on three aspects-the edge-element method

analysis of nonlinear structures and pre-/post-processing problems of the finite element programs

which are considered to represent the developing trends of this field.