A vast number of engineering applications involve physics not solely of a single domain but of several physical phenomena, and therefore are referred to as multi-physical. As long as the phenomena considered are to be treated by either a continuous (i.e. Eulerian) or discrete (i.e. Lagrangian) approach, numerical solution methods may be employed to solve the problem. However, numerous challenges in engineering exist and evolve; those include modelling a continuous and discrete phase simultaneously, which cannot be solved accurately by continuous or discrete approaches only. Problems that involve both a continuous and a discrete phase are important in applications as diverse as the pharmaceutical industry, the food processing industry, mining, construction, agricultural machinery, metals manufacturing, energy production and systems biology. A novel technique referred to as Extended Discrete Element Method (XDEM) has been developed that offers a significant advancement for coupled discrete and continuous numerical simulation concepts. XDEM extends the dynamics of granular materials or particles as described through the classical discrete element method (DEM) to include additional properties such as the thermodynamic state or stress/strain for each particle coupled to a continuous phase such as a fluid flow or a solid structure. Contrary to a continuum mechanics concept, XDEM aims at resolving the particulate phase through the various processes attached to particles. While DEM predicts the spatial-temporal position and orientation for each particle, XDEM additionally estimates properties such as the internal temperature and/or species distribution during drying, pyrolysis or combustion of solid fuel material such as biomass in a packed bed. These predictive capabilities are further extended by an interaction with fluid flow by heat, mass and momentum transfer and the impact of particles on structures.