This talk will concern the three dimensional half-wave maps equation (HWM), a nonlocal geometric equation arising in the study of integrable spin systems. In high dimensions, n≥4, the equation is known to admit global solutions for suitably small initial data, however the extension of these results to three dimensions presents significant difficulties due to the loss of a key Strichartz estimate. In this talk I will introduce the half-wave maps equation and discuss a global wellposedness result for the three dimensional problem under the assumption that the initial data has angular regularity. The proof combines techniques from the study of wave maps with new microlocal arguments involving commuting vector fields and improved Strichartz estimates.