Anisotropy graded media is promising to overcome the writability problem in achieving ultrahigh areal density for magnetic recording media. To more conveniently study and compare various media with regard to a particular figure of merit, a new energy landscape method of analysis is suggested. Using this method, the theoretical limit of the figure of merit for a graded medium is found to be 4. This limit can be approached by a graded medium with anisotropy quadratically increasing from zero to its maximum value. In order to characterize the anisotropy distribution of a graded medium, hard axis loops of graded media with various anisotropy profiles are simulated and analyzed. It is found that the second derivative of the hard axis loop can give useful information on the anisotropy distribution in a graded medium. Fe₅₀Pt₅₀ with the L1₀ structure, as one of the magnetically hardest materials, has great potential for media application. By using a first-principles calculation method, the magnetic and electronic structures of L1₀ structured Fe₅₀Pt₅₀ have been studied. These calculations show that although the ferromagnetic phase is the most stable phase for Fe₅₀Pt₅₀ with the L1₀ structure, there is a competition between the antiferromagnetic and the ferromagnetic phases when the ratio of lattice constants, c/a, decreases. Experimental investigations of Fe₅₀Pt₅₀ films with graded order parameter fabricated by varying the growth temperature during deposition demonstrate that these films have much smaller switching field than fully ordered Fe₅₀Pt₅₀, which suggests it is possible to make graded media by using this kind of films. Fe₁₀₋ₓPtₓ films with compositional gradient were also studied; however, the large easy axis dispersion in these films makes them unsuitable for the fabrication of graded media. Films with [FePt₃ordered)/FePt₃ (disordered)]n superlattices were deposited on MgO substrates and sapphire substrates. It was found that the exchange bias in superlattices deposited on MgO substrate show higher exchange bias field. Polarized neutron reflectivity results show that ferromagnetic layers on MgO substrates contain more antiferromagnetic component than those on sapphire substrates. The larger exchange bias of the superlattice on MgO substrate is hypothesized to be due to larger exchange bias in its ferromagnetic layers.