Phase separation in binary liquid Lennard-Jones clusters is investigated employing computer simulation methods. Clusters ranging in size from 50 to 240 particles are considered with special emphasis on systems with equal numbers of A and B particles. Cluster morphology is systematically explored by varying the ratios, alpha=epsilon(AB)/epsilon(AA), beta=epsilon(BB)/epsilon(AA), Gamma=sigma(AB)/sigma(AA), and Delta=sigma(BB)/sigma(AA), where sigma and epsilon are the Lennard-Jones size and energy parameters. A detailed alpha,beta "phase diagram" is presented for the case Gamma=Delta=1. Stable phase separated clusters are shown to fall into two general classes : elongated clusters of cylindrical or dumbbell shape, the ends of which are A-rich and B-rich phases, and spherical coated clusters consisting of a core of one species coated by the other. More quantitative structural information is given in the form of interfacial density profiles. We also propose two theoretical models for phase separation in binary clusters. One is a simple macroscopiclike droplet approach and the other is a mean field lattice model. Both simple models capture many of the important physical features observed in the computer simulations. Together they provide insight into the nature of phase separation in small systems.