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For decades, theoretical models have struggled to account for the observed levels of tidal dissipation in giant planets and solar-type stars --- objects with substantial convective envelopes. In this talk, I will review these models and show that they fail in the regime of rapid tides, where the tidal period is shorter than the convective turnover timescale. I will then introduce a new approach that applies in this limit. By assuming that tidal energy is transferred to the convective flow, the resulting predictions for the tidal dissipation factor in Jupiter and Saturn, as well as for the circularization periods of solar-type binaries and exoplanets, are broadly consistent with observational data.