Presently, dedicated instruments at large telescopes (SPHERE for the VLT, GPI for Gemini) are about to discover and explore self- luminous giant planets by direct imaging and spectroscopy. The next generation of 30m-40m ground-based telescopes, the Extremely Large Telescopes (ELTs), have the potential to dramatically enlarge the discovery space towards older giant planets seen in reflected light and ultimately even a small number of rocky planets. EPICS is a proposed instrument for the European ELT, dedicated to the detection and characterization of Exoplanets by direct imaging, spectroscopy and polarimetry. ESO completed a phase-A study for EPICS with a large European consortium which - by simulations and demonstration experiments - investigated state-of-the-art diffraction and speckle suppression techniques to deliver highest contrasts. The paper presents the instrument concept and analysis as well as its main innovations and science capabilities. EPICS is capable of discovering hundreds of giant planets, and dozens of lower mass planets down to the rocky planets domain.