Ultrathin magnetic films grown on atomically stepped surfaces exhibit many interesting properties due to the lateral modulation at the nanometer scale. To systematically control the atomic steps curved substrates are utilized to provide a continuous range of step density. Fe and Co films grown on curved Ag(001), W(001) and Cu(001) have been investigated by means of the surface magneto-optic Kerr effect. The atomic steps induce an in-plane, uniaxial magnetic anisotropy with the easy axis either parallel or perpendicular to the step edges. The strength of the step-induced anisotropy is linearly roportional to step density for fcc magnetic films, but scales quadratically for bcc magnetic films. The Neel pair-bonding model provides a possible explanation for these observations. Even more intriguing results occur when substrate magnetism is induced at the stepped interface, as for the Fe/Pd(001) system. The ferromagnetic nature of the interfacial fcc Pd dominates the anisotropy to result in a linear dependence of the step-induced anisotropy on step density even though the Fe overlayer is bcc. The step-induced moment in this system is also shown to enhance the Curie temperature. Finally, for the Fe/Cr(001) system, the compensated, stepped Cr(001) surface is found to produce a 90-degree coupling between the Fe and Cr moments. When this effect competes with the step-induced anisotropy, the Fe magnetization undergoes an in-plane spin-reorientation transition from perpendicular to parallel to the step edges with increasing step density.