This paper deals with regularization techniques developed in order to overcome the strongly singular (displacement BIE) or hypersingular (traction BIE) character of the boundary integral equations commonly used for three-dimensional ëlastodynamics. More specifically, we address indirect regularization techniques, which rely upon singularity exclusion and separate evaluation of strongly singular or hypersingular integrals containing the singular kernel only. In many, but not all, cases, this evaluation can be made using an auxiliary static problem together with the fact that the dynamic and static kernels share the same singular term. In this paper we first give a bibliographical outline of the regularization problem. Then the regularized displacement and traction BIE for general 3D situations in transient ëlastodynamics, including crack problems, are derived and stated. We also recall related results of interest. Then numerical implementation considerations are considered. For completeness, a brief survey of Galerkin-type and direct approaches is also given. Finally some numerical examples in ëlastodynamics are given.