We study the kinetics of diffusion-limited coalescence, A+A --> A, and annihilation, A+A --> 0, in random media consisting of disconnected domains of reaction. Examples include exciton fusion and annihilation in porous matrices and along polymer chains. We begin with an exact analysis of A+A --> A in a finite segment. This result is applied to coalescence in a random distribution of segment lengths, and the implications for coalescence and annihilation in percolation clusters and other confined geometries are then derived by means of scaling techniques.