In this work we propose an overview of results about propagation of waves and elasticity in soils over the last 30 years. Remarkably, the chapter attempts to frame and compare contributions from soil mechanics, solid mechanics and physics. In a wide landscape, we focus on the micromechanical approach to the topic. Numerical simulations, based on the Discrete Element Method, have revealed the outmost role of the microstructure in characterising the elastic behaviour of granular soils. Following this evidence, microstructure-based continuum models have been developed and are discussed here, starting from the classical Effective Medium Theory. Finally, the chapter describes how micromechanical models can be extended to the case of immersed granular soils, and compares the new model with experiments on sand soils in a wide range of saturation degrees.