The scaled boundary finite element method (SBFEM) has been developed into a general purpose numerical method since it was first proposed by Song and Wolf in 1996 for the solution of wave propagation problems. This method is semi-analytical and only the boundaries of the subdomains are discretized. Its advantages were firstly recognized for the modelling of problems involving unbounded media and singularities. Recently, a methodology for constructing arbitrary polygon/polyhedron elements for linear and nonlinear analyses was established based on the SBFEM. This development theoretically renders the range of application of the SBFEM as wide as that of the displacement-based finite element method. Today, the application of the SBFEM has been expanded to many other important fields in engineering, such as fluid mechanics, electrostatics, sensitivity analysis and heat transfer. However, great potential of the SBFEM in modelling 3D microstructures of concrete or composite materials, crack propagation, dynamic contact for cracks analysis, moving boundary problems, etc. remains to be explored.