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Cavitation is often triggered when the fluid pressure is lower than the vapor pressure at a local thermodynamic state. The present article reviews recent progress made toward developing modeling and computational strategies for cavitation predictions under both isothermal and cryogenic conditions, with an emphasis on the attached cavity. The review considers alternative cavitation models along Reynolds-averaged Navier-Stokes and very lager eddy simulation turbulence approaches to ensure that the computational tools can handle flows of engineering interests. Observing the substantial uncertainties associated with both modeling and experimental information, surrogate modeling strategies are reviewed to assess the implications and relative importance of the various modeling and materials parameters. The exchange between static and dynamic pressures under the influence of the viscous effects can have a noticeable impact on the effective shape of a solid object, which can impact the cavitation structure. The thermal effect with respect to evaporation and condensation dynamics is examined to shed light on the fluid physics associated with cryogenic cavitation. The surrogate modeling techniques are highlighted in the context of modeling sensitivity assessment.