As systems and technologies become increasingly complex, the models that are vital to their design and development must balance the need to capture this complexity at an acceptable computational cost. The terahertz (THz) frequency range of the electromagnetic spectrum, perhaps the last frontier, takes engineers into new realms of highly non-linear and strongly radiating behaviours. Modelling these efficiently and accurately requires application of so-called time-domain boundary element methods (TD-BEMs), which are currently not as mature as other approaches. The EU-funded BET3D project is accelerating the development of TD-BEMs to support a new generation of THz technologies with applications in key fields including medicine, security and energy.