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The complex patterns of the hadronic spectrum have puzzled physicists sincethe early discovery of the "particle zoo" in the 1960s. Today, the propertiesof these myriad particles are understood to be the result of quantumchromodynamics (QCD) with some modification by the electroweak interactions.Despite the discovery of this fundamental theory, the description of thehadronic spectrum has long been dominated by phenomenological models, due tothe difficulties of addressing QCD in the strong-coupling regime, wherenonperturbative effects are essential. By making numerical calculations indiscretized spacetime, lattice gauge theory enables the ab initio study of manylow-energy properties of QCD. Significant efforts are underway internationallyto use lattice QCD to directly compute properties of ground and excited-statebaryons. Detailed knowledge of the hadronic spectrum will provide insight intothe character of these states beyond what can be extracted from models.  In this review, I will focus on the latest progress in lattice calculationsof the $P_{11}(1440)$, the poorly known hyperon spectrum and the energies ofhighly-excited states of the nucleon, Delta and other light-flavor baryons. Inthe heavy-flavor sector, I will concentrate on recent lattice-QCD calculationsof baryon masses, particularly those that make predictions concerningyet-to-be-discovered baryons, such as $\Omega_{cc}$, $\Xi^\prime_b$ ortriply-heavy baryons.

Review of Baryon Spectroscopy in Lattice QCD