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We describe general features of frequency-dependent charge transport near strongly interacting quantum critical points in 2+1 dimensions. The simplest description using the AdS/CFT correspondence leads to a self-dual Einstein-Maxwell theory on AdS_4, which fixes the conductivity at a frequency-independent self-dual value. We describe the general structure of higher-derivative corrections to the Einstein-Maxwell theory, and compute their implications for the frequency dependence of the quantum-critical conductivity. We show that physical consistency conditions on the higher-derivative terms allow only a limited frequency dependence in the conductivity. The frequency dependence is amenable to a physical interpretation using transport of either particle-like or vortex-like excitations.