<p>We consider local values in both classical physics and quantum mechanics. We first formulate the concept in classical physics using two equivalent approaches, and then attempt to apply the same procedure to local values in quantum mechanics. We briefly review the phase-space formulation of quantum mechanics, one of the standard approaches for obtaining local values. We discuss the transformation of variables for a standard probability distribution and contrast it with the transformation of quasi-distributions. We show that the transformation of variables for quasi-distributions does not work in the usual sense; it does not yield the correct quantum-mechanical marginals of the new variables. We therefore derive new quasi-distributions that indeed do satisfy the marginals and use them to obtain local values. In classical physics, local values are representable, that is, well defined, since they are derived from proper probability densities. However, in quantum mechanics, the corresponding quantities are generally not representable and often exhibit very peculiar behavior. In the classical case, one also considers the standard deviation of a local quantity. In the quantum case, their standard deviations have generally not been discussed, and we emphasize this issue in the present paper. Also, since there are infinitely many quasi-distributions, there are an infinite number of local values. We obtain explicit transformation equations for local values defined by different quasi-distributions.</p>