ABSTRACT Recent years have witnessed rapid progress in observations of the epoch of reionization (EoR). These have enabled high-dimensional inference of galaxy and intergalactic medium (IGM) properties during the first billion years of our Universe. However, even using efficient, seminumerical simulations, traditional inference approaches that compute 3D lightcones on-the-fly can take 105 core hours. Here we present 21cmemu: an emulator of several summary observables from the popular 21cmfast simulation code. 21cmemu takes as input nine parameters characterizing EoR galaxies, and outputs the following summary statistics: (i) the IGM mean neutral fraction; (ii) the 21-cm power spectrum; (iii) the mean 21-cm spin temperature; (iv) the sky-averaged (global) 21-cm signal; (vi) the ultraviolet (UV) luminosity functions (LFs); and (vii) the Thomson scattering optical depth to the cosmic microwave background (CMB). All observables are predicted with sub- per cent median accuracy, with a reduction of the computational cost by a factor of over 104. After validating inference results, we showcase a few applications, including: (i) quantifying the relative constraining power of different observational data sets; (ii) seeing how recent claims of a late EoR impact previous inferences; and (iii) forecasting upcoming constraints from the sixth observing season of the Hydrogen Epoch of Reionization Array (HERA) telescope. 21cmemu is publicly available, and is included as an alternative simulator in the public 21cmmc sampler.