This Key Note presents a summary of the development of the Finite Element Method in the field of Electromagnetic Engineering, together with a description of several contributions of the authors to the Finite Element Method and its application to the solution of electromagnetic problems. First, a self-adaptive mesh scheme is presented in the context of the quasi-static and full-wave analysis of general anisotropic multiconductor arbitrary shaped waveguiding structures. A comparison between two a posteriori error estimates is done. The first one is based on the complete residual of the differential equations defining the problem. The second one is based on a recovery or smoothing technique of the electromagnetic field. Next, an implementation of the first family of Nédélec's curl-conforming elements done by the authors is outlined. Its features are highlighted and compared with other curl-conforming elements. A presentation of an iterative procedure using a numerically exact radiation condition for the analysis of open (scattering and radiation) problems follows. Other contributions of the authors, like the use of wavelet like basis functions and an implementation of a Time Domain Finite Element Method in the context of two-dimensional scattering problems are only mentioned due to the lack of space.