The scaled boundary finite element method (SBFEM) has recently gained popularity as a rather general tool for numerical analyses, i.e., the solution of partial differential equations in complex domains. Current approaches exploit the flexibility of this method concerning mesh generation since it allows elements (subdomains) of any size that may consist of an arbitrary number of vertices and edges. The current contribution focuses on issues related to the application of this method to dynamics and wave propagation phenomena since there are still a number of open questions in this field. As the semi-analytical equations obtained in the SBFEM do not allow a straightforward (analytical) solution for arbitrary frequencies, several different approaches have been proposed in the literature to approximate the dynamic response and achieve optimal convergence. Furthermore, additional aspects need to be considered when modeling bounded or unbounded domains. These techniques are discussed and evaluated for their application in the frequency domain as well as for implicit and explicit transient analyses.