General approaches for developing models to describe the elastic properties of granular and porous materials are discussed, with emphasis on their application to predicting the elastic properties of powders undergoing uniaxial compaction. Both particle-based, and pore-based models were considered so as to reflect the transition in compact response with decreasing porosity; being particle-dominated at high porosity, then pore-dominated at low porosity. Pore-based models were further subdivided into: mechanistic models, which consider the effects of porosity on internal mechanical fields; and geometric models, for which the elastic response is assumed to correlate with a microstructural feature (e.g. load-bearing area). A selection of models suggested in the literature, considered representative of these approaches, was applied to experimental measurements of the elastic moduli of powders during compaction. In general, the geometric pore-based models show most promise, as these are able to approximate the transition in pore character during compaction. However, further developments are required for application to uniaxially compacted powders. In particular, it is necessary to develop the ability to predict more than one elastic modulus, handle irregular powder particles, and accommodate powders comprised of brittle solid phase materials.