ABSTRACT We explore the survival of cool clouds in multiphase circumgalactic media. We revisit the ‘cloud-crushing problem’ in a large survey of simulations including radiative cooling, self-shielding, self-gravity, magnetic fields, and anisotropic Braginskii conduction and viscosity (with saturation). We explore a wide range of parameters including cloud size, velocity, ambient temperature and density, and a variety of magnetic field configurations and cloud turbulence. We find that realistic magnetic fields and turbulence have weaker effects on cloud survival; the most important physics is radiative cooling and conduction. Self-gravity and self-shielding are important for clouds that are initially Jeans-unstable, but largely irrelevant otherwise. Non-self-gravitating, realistically magnetized clouds separate into four regimes: (1) at low column densities, clouds evaporate rapidly via conduction; (2) a ‘failed pressure confinement’ regime, where the ambient hot gas cools too rapidly to provide pressure confinement for the cloud; (3) an ‘infinitely long-lived’ regime, in which the cloud lifetime becomes longer than the cooling time of gas swept up in the leading bow shock, so the cloud begins to accrete and grow; and (4) a ‘classical cloud destruction’ regime, where clouds are eventually destroyed by instabilities. In the final regime, the cloud lifetime can exceed the naive cloud-crushing time owing to conduction-induced compression. However, small and/or slow-moving clouds can also evaporate more rapidly than the cloud-crushing time. We develop simple analytic models that explain the simulated cloud destruction times in this regime.