Active sound reduction is the use of active sources of sound, that is devices which are potentially sources of sound energy, to modify a preexisting sound field in such a way that the overall effect is a reduction in sound. Until recently the most common approach in active sound control was to attempt to achieve complete cancellation of the sound. This is possible at single points but is practically impossible over an appreciable region. A more modest and practical aim is to try to reduce the sound field by as much as possible by minimizing some overall measure of the amplitude of the sound field. This thesis examines the technique of sound field minimization. Candidate sound field measures which are suitable for minimization are presented and discussed. The quantities include acoustic energy, intensity and power flow as well as a practical measure, the sum of the squares of the signals from a number of sensors. Theoretical simulations and experimental implementations are used to evaluate sound field minimization techniques. The discussion and experiments are extended to the active reduction of structural vibrations.