This work presents a coupling technique to combine the Boundary Element Method (BEM) and the Discrete Element Method (DEM) to model dynamic problems in infinite media. The simulation of real-life engineering problems usually requires capturing several physical phenomena. The simulation must be able to capture complex material behaviours such as the ones observed in granular materials and rock. In addition, it is necessary to represent wave propagation, which often occurs in unbounded domains. However, in most simulations, complex material behaviours are mobilised in a small portion of the domain, called the near-field region. On the other hand, the far-field region is far from any source discontinuities, where propagating waves dominate the wave behaviour. In this region, the wave amplitude decreases with the distance from the source and the wavefronts become regular and well-defined. Both methods utilised in this work offer excellent modelling capabilities relevant to simulating real-life engineering problems. As the DEM models the interactions between individual particles, it excels in capturing highly nonlinear behaviour in both physical and geometric aspects. In contrast, the BEM excels in representing wave propagation, especially in infinite domains where other continuum-based and particle-based methods face challenges. Therefore, the coupled BEM-DEM offers a powerful modelling tool for simulating real-life dynamic problems in infinite media. The DEM represents the near-field, while the BEM represents the far-field. This work discusses how to treat the difficulties arising from the different time integration in each method [1] and the incompatibilities between point-loads and distributed tractions [2]. The compatibility condition of displacements at nonconforming interfaces is also discussed. The monolithic and staggered approaches are implemented and compared regarding the time integration of interface conditions. Several numerical experiments are included to demonstrate the accuracy and efficiency of the coupled solution.