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Abstract
Photoionized clouds are ubiquitous. They define the endpoints of stellar evolution (H II regions and planetary nebulae), constitute the interstellar and intergalactic media, and are found in high redshift quasars and star-forming galaxies. The spectra of these objects are dominated by emission lines that are sensitive to details of the emitting gas. These details include the microscopic atomic processes that cause the gas to glow; the density, composition, and temperature of the gas; and the radiation field of the central continuum source. Large-scale numerical codes that incorporate all the needed physics and predict the observed spectrum have become essential tools in understanding these objects. This article reviews the current status of the numerical simulations of emitting gas, with particular emphasis on photoionized clouds and the underlying simplicity that governs these nebulae; the types of questions that can be addressed by today's codes; and the big questions that remain unanswered.