Over the last half-century, computational electromagnetics has become a very important analytical tool in electronics, photonics, wireless communication and imaging technologies. Time-domain integral equations have emerged as the most predominant approach to deal with complex problems, especially for modelling unbounded, nonlinear and radiating systems. Unfortunately, time-domain integral equation methods are not nearly as mature as those from other classes. Attempts to model realistic complex systems using time-domain integral equations result in various numerical issues, which render the solution completely useless or lead to prohibitively long simulation times. The rapidly rising variety of electromagnetic applications, as well as their increasing complexity, has accelerated the critical need for studies of robust, stable and highly efficient time-domain integral equation methods. Without the development of such methods, the considerably high cost of designing next-generation systems will be impediments to further advancements in computational electromagnetics. This research project aims to develop and implement a scalable time-domain integral equation solver that is highly efficient. The developed methods will enable the capacity to model and analyze transient radiation, multi-physics and nonlinear systems, which are increasingly present in cutting-edge technologies and applications.