The discrete nature of granular materials results in myriad complex behaviors that are not readily described by continuum mechanics even though it may be tempting to treat them as continua when considering spatial scales that are large relative to some mean particle size. Treating granular assemblies as continua can result in models that fail to predict emergent phenomena or capture the inherent interplay between phases (air, water, solid), processes (thermal, hydraulic, mechanical), and scales (particle, specimen, design) that fully describe material behavior. This talk will present an overview of some of the mathematical and physical complexities of granular materials and describe approaches for simulating granular assemblies at the particle scale. Relationships between particle behavior and assembly behavior will be presented. A model for thermal conduction in granular media will serve as a practical example and provide insight into percolation in binary mixtures.