This book is a comprehensive assessment of the various theoretical and numerical methods currently in use to investigate microstructural transformations and mechanical properties of inhomogeneous systems, from the atomic scale to the macroscopic: kinetic mean-field theories, Monte Carlo and molecular dynamics simulations, Ginzburg-Landau and phase field methods as applied to plasticity and microstructure transformation, discrete and stochastic dislocation dynamics, and cluster dynamics. Extensive surveys of major physical processes include: solidification, microstructural evolution in single and polycrystalline systems under internal and applied stress, high temperature plasticity, recrystallization, large plastic strain in multiphase systems, fatigue, fracture, diffusive transformations, and fine grained materials.