There is a well-known simple formula for computing local volatility given implied volatility as a function of strike and expiration. Given local volatilities, implied volatilities may be computed numerically using numerical PDE techniques. However, such computations are typically too time-consuming to permit fast calibration of local volatilities to option prices. In this talk, we review various methods that have been proposed for computing implied volatility from local volatility including heat kernel-based expansions and parameter averaging. We focus in particular on the most-likely-path approximation showing by specific example that it tends to perform better in practice than competing approximations.