This work presents different global and local optimization techniques for designing "approximate" circuits which decrease energy consumption, one of the most important criteria in present day circuit design. The concept of "approximate" circuits which trades off energy consumption to output quality, thus creating a new dimension to the design space, is radically different from the conventional design principle in which all circuits operate correctly all the time. But efficient and intelligent designs have to be realized to tap its full potential. These techniques, which have not been explored till date, are based on a rigorous mathematical model and target to improve the output quality of a given circuit keeping the energy consumption to a minimum. They use the value of information and the architecture of the circuit to maximize efficiency. They have been applied to digital signal processing circuits to realize energy savings up to 2X the conventional value.