The Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature. Further, amorphous microclusters are prepared by a Monte Carlo quench, and their structural properties are examined. The properties of interest include the internal energy, instantaneous “snapshot” pictures of the microcluster's atomic configuration, and the single-particle and pair distribution functions. The Lennard-Jones potential parameters are chosen to model Ar 13, Ar 7Kr 6, Ar 36Kr 19 and Ar 19Kr 36, as well as to crudely model the bimetallic clusters of Cu 19Ni 36, Cu 19Ru 36 and Cu 19Os 36. A large variety of interesting features associated with these systems are described.