We have examined the physics and the experimental feasibility of studying various kaon decay processes in which the polarization of a muon in the final state is measured. Valuable information on CP violation, the quark mixing (CKM) matrix, and new physics can be obtained from such measurements. We have considered muon polarization in KL→μ+μ- and K→πμ+μ- decays. Although the effects are small, or difficult to measure because of the small branching ratios involved, these studies could provide clean measurements of the CKM parameters. The experimental difficulty appears comparable to the observation of [Formula: see text]. New sources of physics, involving nonstandard CP violation, could produce effects observable in these measurements. Limits from new results on the neutron and electron electric dipole moment, and [Formula: see text] in neutral kaon decays, do not eliminate certain models that could contribute to the signal. A detailed examination of muon polarization out of the decay plane in K+→μ+π0ν and K+→μ+νγ decays also appears to be of interest. With current kaon beams and detector techniques, it is possible to measure the T-violating polarization for K+→μ+π0ν and with uncertainties approaching ~10-4. This level of sensitivity would provide an interesting probe of new physics.