We present the simultaneous Swift and Fermi observations of the bright GRB 100728A and its afterglow. The early X-ray emission is dominated by a vigorous flaring activity continuing until 1 ks after the burst. In the same time interval, high-energy emission is significantly detected by the Fermi/Large Area Telescope. Marginal evidence of GeV emission is observed up to later times. We discuss the broadband properties of this burst within both the internal and external shock scenarios, with a particular emphasis on the relation between X-ray flares, the GeV emission, and a continued long-duration central engine activity as their power source.