In this chapter, the two principal approaches in coevolution—competitive and cooperative—will be elaborated further. The presentation will focus on key implementation details of these two coevolutionary approaches. The section following the general introduction will provide algorithmic descriptions through two general frameworks, each encapsulating one of the two coevolutionary approaches. They provide the means to differentiate these two approaches through their main distinguishing features involving specific interactions in the populations. This is then followed by discussion of implementation details of these Coevolutionary Algorithms for problem solving in the context of learning and optimization. The last section closes with remarks on coevolutionary systems that incorporate both competitive and cooperative mechanisms, making use of the general frameworks introduced earlier to indicate how both mechanisms can be synergistically exploited and combined.