Most fish are indeterminate growers with white muscle making up the majority of the acquired bulk. Within the muscle, the myofibrillar fraction accounts for almost two-thirds of the protein synthetic activity, implying that it is accretion of myofibrillar proteins that makes the single most important contribution to fish growth. Fish muscle growth itself is not linear and occurs through a combination of hyperplasia and hypertrophy in post-juvenile stages. Superimposed on periodicity of growth in length and mass can be other phases governed by lunar, reproductive or circannual cycles. Data on fish growth are discussed in the framework of site-specific muscle abundance, metabolic and functional zonation of muscle, proliferation and differentiation of satellite cells and the contribution of myofibrillar proteins. Hormonal control of muscle growth is described against the backdrop of plasma availability of myogens (insulin, IGF-I, growth hormone), distribution and dynamics of their respective receptors, and their interactions. Important contributions of the 'supply side' are discussed with hormones regulating amino acid resorption from the intestine, intestinal growth, liver processing and amino acid uptake by the muscle. Data are also interpreted from metabolic angles, to explain lipolytic and nitrogen-sparing effects of growth hormones, and lipogenic effects of insulin and high protein diets. Finally, special attention is devoted to the multifaceted roles of arginine in fish growth, as precursor, intermediate and hormone secretagogue.