For decades, the unnaturalness of the weak scale has been the dominant problem motivating new particle physics, and weak-scale supersymmetry has been the dominant proposed solution. This paradigm is now being challenged by a wealth of experimental data. In this review, we begin by recalling the theoretical motivations for weak-scale supersymmetry, including the gauge hierarchy problem, grand unification, and WIMP (weakly interacting massive particle) dark matter, and their implications for superpartner masses. These are set against the leading constraints on supersymmetry from collider searches, the Higgs boson mass, and low-energy constraints on flavor and CP violation. We then critically examine attempts to quantify naturalness in supersymmetry, stressing the many subjective choices that influence the results both quantitatively and qualitatively. Finally, we survey various proposals for natural supersymmetric models, including effective supersymmetry, focus point supersymmetry, compressed supersymmetry, and R-parity-violating supersymmetry, and summarize their key features, current status, and implications for future experiments. © Copyright ©2013 by Annual Reviews. All rights reserved.