This review deals with biomechanical aspects of growth (mass change), remodeling (property change), and morphogenesis (shape change) in living systems. The emphasis is on theoretical models, but relevant experimental results also are discussed. As an aid to the reader, the fundamental biological terms and concepts are defined for the general problem and for each specific topic. At the outset, the processes involved in growth, remodeling, and morphogenesis are described and placed within the context of the evolution of species. Next, some of the analytical methods used in biomechanical models for these processes are presented. Then, applications of these and other techniques to specific systems are discussed, beginning at the cellular level and proceeding upward to the tissue and organ levels. At the cellular level, modeling and experimental studies are reviewed for cell division, cell movement, and pattern formation, and then morphogenetic mechanisms for epithelia (cell sheets) are discussed. At the tissue and organ levels, the musculoskeletal and cardiovascular systems are considered. Several models are described for growth, remodeling, and morphogenesis of bone, and mainly experimental results are examined in the cases of skeletal muscle, the heart, and arteries. Specific topics for the cardiovascular system include hypertrophy, residual stress, atherosclerosis, and embryonic development. Finally, some future research directions are suggested.