Amino acid availability is a rate-limiting factor in the regulation of protein synthesis. When amino acid supplies become restricted, mammalian cells employ homeostatic mechanisms to rapidly inhibit processes such as protein synthesis, which demands high levels of amino acids. Muscle cells in particular are subject to high protein turnover rates to maintain amino acid homeostasis. Mammalian target of rapamycin complex 1 (mTORC1) is an evolutionary conserved multiprotein complex that coordinates a network of signaling cascades and functions as a key mediator of protein translation, gene transcription, and autophagy. Signal transduction through mTORC1, which is centrally involved in muscle growth through enhanced protein translation, is governed by intracellular amino acid supply. The branched-chain amino acid leucine is critical for muscle growth and acts in part through activation of mTORC1. Recent research has revealed that mTORC1 signaling is coordinated primarily at the lysosomal membranes. This discovery has sparked a wealth of research in this field, revealing several different signaling molecules involved in transducing the amino acid signal to mTORC1, including the Rag GTPases, MAP4K3, and Vps34/ULK1. This review evaluates the current knowledge regarding cellular mechanisms that control and sense the intracellular amino acid pool. We discuss the role of leucine and mTORC1 in the regulation of amino acid transport via the system L and system A transporters such as LAT1 and SNAT2, as well as protein degradation via autophagic and proteasomal pathways. We also describe the complexities of energy homeostasis via AMPK and cell receptor-mediated growth signals that also converge on mTORC1. Leucine is a particularly potent regulator of protein turnover, to the extent where leucine stimulation alone is sufficient to stimulate mTORC1 signal transduction. The significance of leucine in this context is not yet known; however, recent advancements in this area will also be covered within this review.