We will discuss our recent results with active nematic liquid crystals on toroidal surfaces and show how, despite the intrinsic activity and out-of-equilibrium character of our system, we still observe remnants of the expected curvature-induced defect unbinding predicted for nematics in their ground state. In our experiments, however, the number of defects is far larger than what one would expect for conventional nematics. In addition, these defects move throughout the toroidal surface and arrange in unexpected ways when compared to conventional nematics. Comparing our results to numerical simulations, we unravel the key role of activity in these findings via defect creation and annihilation events.