It is well-known that the usage of a fundamental solution permits in the boundary element method to reduce the dimension of spatial discretization by one. Another striking feature of the boundary element method is that the radiation condition at infinity is satisfied exactly when modeling unbounded media. However, in dynamics the fundamental solution can be very complicated or is not even available for general anisotropic materials. In contrast, the finite element method, which does not require a fundamental solution, is more versatile, but requires the spatial discretization of the domain. In addition, when modelling unbounded media, the radiation condition can, in general, be satisfied only approximately. The novel scaled boundary finite-element method is a fundamental solution-less boundary element method based on finite elements, which combines the advantages of boundary element and finite element methods. It is the main goal of this paper to present the state-of-the-art of the scaled boundary finite element method. Formulation for body loads is also included. Elastodynamics is used as an example. The scaled boundary finite-element equation in displacements is solved analytically as a power series in a dimensionless frequency. The dynamic stiffness matrices of bounded and unbounded media are also determined analytically. The authors compare the features of the scaled boundary finite-element method with those of the boundary element and finite element methods.