We study edge states in two two-dimensional systems of present theoretical and experimental interest. The first platform is a graphene-ferromagnet system. The proximity-induced couplings in graphene due to the vicinity of a ferromagnetic insulator with significant spin-orbit coupling are analyzed. We combine general symmetry principles and simple tight-binding descriptions to consider different orientations of the magnetization. We find that, in addition to a simple exchange field, a number of other terms arise. Some of these terms act as magnetic orbital couplings, and others are proximity-induced spin-orbit interactions. The couplings are of similar order of magnitude, and depend on the orientation of the magnetization. A variety of phases, and anomalous Hall effect regimes, are possible. Engineering these interaction terms to control spin transport in a specific material is important for spintronics applications. The second platform is a two-dimensional p-wave superconductor. We analyze the formation of Majorana zero-modes at the edge of a two-dimensional topological superconductor. In particular, we study a time-reversal-invariant triplet phase that is likely to exist in doped Bi2Se3. Upon the introduction of an in-plane magnetic field to the superconductor, a gap is opened in the surface modes, which induces localized Majorana modes. The position of these modes can be simply manipulated by changing the orientation of the applied field, yielding novel methods for braiding these states with possible applications to topological quantum computation.