HARMONI has been conceived as a workhorse visible and near-infrared (0.47-2.45 microns) integral field spectrograph for the European Extremely Large Telescope (E-ELT). It provides both seeing and diffraction limited observations at several spectral resolutions (R= 4000, 10000, 20000). HARMONI can operate with almost any flavor of AO (e.g. GLAO, LTAO, SCAO), and it is equipped with four spaxel scales (4, 10, 20 and 40 mas) thanks to which it can be optimally configured for a wide variety of science programs, from ultra-sensitive observations of point sources to highangular resolution spatially resolved studies of extended objects. In this paper we describe the expected performance of the instrument as well as its scientific potential. We show some simulated observations for a selected science program, and compare HARMONI with other ground and space based facilities, like VLT, ALMA, and JWST, commenting on their synergies and complementarities.