The complete fusion of light, weakly-bound nuclides is known to be significantly suppressed with respect to comparable well-bound projectiles or with respect to single barrier penetration model calculations. Strong α-clustering in these light systems mean that they very easily disintegrate into clusters, either via direct excitation of their intrinsic cluster continuum, or via transfer reactions which connect to unbound states in neighbouring nuclides. This breakup is thought to reduce the probability for complete fusion. Here we discuss which processes cause breakup, whether or not breakup happens fast enough, and the interpretation of measurements made at the Australian National University of breakup using classical dynamical models. Understanding the intimate details of breakup, and the resonances through which it proceeds, will be crucial in determining its likely influence on fusion.