  This paper discusses the practical development of space-time boundary element
methods for the wave equation in three spatial dimensions. The employed trial
spaces stem from simplex meshes of the lateral boundary of the space-time
cylinder. This approach conforms genuinely to the distinguished structure of
the solution operators of the wave equation, so-called retarded potentials.
Since the numerical evaluation of the arising integrals is intricate, the bulk
of this work is constituted by ideas about quadrature techniques for retarded
layer potentials and associated energetic bilinear forms. Finally, we glimpse
at algorithmic aspects regarding the efficient implementation of retarded
potentials in the space-time setting. The proposed methods are verified by
means of numerical experiments, which illustrate their capacity.
