Recently new reactor antineutrino spectra have been provided for 235U, 239Pu, 241Pu and 238U, increasing the mean flux by about 3 percent. To good approximation, this reevaluation applies to all reactor neutrino experiments. The synthesis of published experiments at reactor-detector distances <100 m leads to a ratio of observed event rate to predicted rate of 0.976(0.024). With our new flux evaluation, this ratio shifts to 0.943(0.023), leading to a deviation from unity at 98.6% C.L. which we call the reactor antineutrino anomaly. The compatibility of our results with the existence of a fourth non-standard neutrino state driving neutrino oscillations at short distances is discussed. The combined analysis of reactor data, gallium solar neutrino calibration experiments, and MiniBooNE-neutrino data disfavors the no-oscillation hypothesis at 99.8% C.L. The oscillation parameters are such that |Delta m_{new}^2|>1.5 eV^2 (95%) and sin^2(2theta_{new})=0.14(0.08) (95%). Constraints on the theta13 neutrino mixing angle are revised.