Rapid follow-up of gamma-ray burst (GRB) afterglows with the multi-wavelength satellite Swift and other instruments is shedding new light on GRB. This is leading to a reappraisal and expansion of the standard model of the GRB early afterglow behavior and its connection to the prompt gamma-ray emission. New information in the previously poorly known time range from minutes to hours has revealed characteristic properties of the X-ray light curves, including steep decays followed by shallow decays and flares. Other discoveries include the localization and follow-up of short GRB afterglows, localizing long bursts beyond the z≳6 redshift range, the detection of prompt optical/IR emission while the burst is still emitting gamma-rays, the detection and prompt follow-up of supernovae associated with GRB, and challenges to the traditional short-long classification. We review some of the current theoretical interpretations of these new phenomena.