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 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 impact 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.Comment: 38 pages, to appear in Annual Review of Nuclear and Particle Science;
v2: fixed typos, updated Higgs results, added references and a parable,
published versio
