The finite element method (FEM) is one of the most versatile methods of numerically analyzing physical phenomena described by partial differential equation. It is suitable to the analysis of such a complicated region which includes non-linear materials. It has some disadvantages, however, in dealing with the field extending infinitely. The phenomena in the electromagnetic field intrinsically spread over the infinite space. We sometimes have to consider the infinite region rigorously, e.g. in the magnetic stray field of superconducting magnets. The boundary element method (BEM) is useful to analyze very large linear fields. It reduces the domain problem to the boundary problem and is particularly suitable for analyzing the infinite space. Furthermore, the required potentials and those derivatives inside the domain are calculated by using theoretical expressions. Owing to these features, the boundary element method is especially useful for the analysis of electromagnetic phenomena. Taking account of advantages in both the finite element and the boundary element methods, the hybrid utilization of both methods (the hybrid FE-BE method) has been proposed. In this review, the recent development and several analytical results of the three-dimensional boundary element method and the hybrid FE-BE method are described.