First principles calculations based upon density functional theory have been used to investigate the magnetic properties of various Fe-Pt and Co-Pt alloys. At the 50:50 composition, the technologically important L10 alloys CoPt and FePt show large magnetocrystalline anisotropies consistent with the natural layering of the crystal structure. Calculated values for the magnetocrystalline anisotropy and magnetizations are found to be in close agreement with measured values. Since the L10 phase forms over a range of compositions, the influence of composition on magnetic properties has also been examined. A simple expression, derived from the Ne´el model, relates the anisotropy to the composition, or degree of disorder in the structure, and is found to be of value for understanding anisotropy in imperfect structures. At greater Fe of Co compositions there are several interesting crystal structures including the metastable pmm2 phase that is composed of alternating pure and mixed planes. Again, fairly large anisotropies are seen as a consequence of layering and symmetry. Growing Fe3Pt pmm2 films seems less promising than Co3Pt pmm2 films given the larger energy difference between the pmm2 and cubic L12 phases.