This chapter will introduce a broad class of evolutionary search approaches that collectively have come to be referred to as Coevolutionary Computation. It starts with a summary account that details developments of several key approaches. The common principle that connects these approaches is noted even though individually they have different motivations underlying their conceptions. The next section unifies these coevolutionary approaches within a common framework and as a result details the principled difference with evolutionary approaches. This is then followed by discussion of main concepts that not only form distinguishing features of these coevolutionary systems but are crucial towards developing mechanisms that support the associated operations in coevolution. The last section closes with remarks on differences and similarities of coevolutionary systems and other methodologies from the field of Machine Learning.