Anisotropic-exchange magnets: triangular lattice and all

I will describe our efforts to understand the phase diagram of a model that combines paradigmatic geometrical frustration of spins on a triangular lattice with strong spin-orbit-induced interactions. This model is relevant to a growing family of rare-earth-based magnets and other related materials and our work sets up a consistent interpretation of the current and future experiments in them. I will also attept to review our recent incursion to the honeycomb-lattice territory and attempts to shed light on the properties of the Kitaev materials such as α-RuCl₃.