This talk will concern the three dimensional half-wave maps equation, a nonlocal geometric equation with close links to the more famous wave maps equation. In high dimensions, it has been known for some years now that the half-wave maps equation admits global solutions for initial data which are sufficiently small in a critical Besov space. The extension of these results to low dimensions, n≤3, presents significant new 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 an additional assumption of angular regularity on the initial data. The proof involves standard techniques from the study of the wave maps equation in combination with a new argument involving commuting vector fields and Sterbenz ‘s improved Strichartz estimates.