Selected orientations of epitaxial Co/Pt superlattices were grown on GaAs substrates in , , and  orientations using seeded epitaxy techniques. The microstructural and magnetic properties of Co/Pt superlattices are presented. The magnetic anisotropies of Co/Pt superlattices are found strongly dependent on the crystallographic orientation of the growth axis. High-resolution cross-sectional transmission electron microscopy (HRXTEM) investigation of the Co/Pt interfaces has revealed the presence of a large number of planar defects in the  Co/Pt superlattice. HRXTEM shows that the interface of Co/Pt is wavy and is not atomically abrupt. These findings suggest that models for the magnetic anisotropy should not be based on idealized, chemically abrupt interfaces but should incorporate magnetocrystalline anisotropy in the alloy region. We propose a model for the magnetic anisotropy based on the N6el magnetic surface anisotropy and the existence of defects in the alloy region. The easy axis of the magnetic anisotropy predicted by the model agrees with the magnetic and structural data for the superlattices.