Particle acceleration and loss in the million electron Volt (MeV) energy range (and above) is the least understood aspect of radiation belt science. In order to measure cleanly and separately both the energetic electron and energetic proton components, there is a need for a carefully designed detector system. The Relativistic Electron-Proton Telescope (REPT) on board the Radiation Belt Storm Probe (RBSP) pair of spacecraft consists of a stack of high-performance silicon solid-state detectors in a telescope configuration, a collimation aperture, and a thick case surrounding the detector stack to shield the sensors from penetrating radiation and bremsstrahlung. The instrument points perpendicular to the spin axis of the spacecraft and measures high-energy electrons (up to ∼20 MeV) with excellent sensitivity and also measures magnetospheric and solar protons to energies well above E=100 MeV. The instrument has a large geometric factor (g=0.2 cm2 sr) to get reasonable count rates (above background) at the higher energies and yet will not saturate at the lower energy ranges. There must be fast enough electronics to avert undue dead-time limitations and chance coincidence effects. The key goal for the REPT design is to measure the directional electron intensities (in the range 10−2–106 particles/cm2 s sr MeV) and energy spectra (ΔE/E∼25 %) throughout the slot and outer radiation belt region. Present simulations and detailed laboratory calibrations show that an excellent design has been attained for the RBSP needs. We describe the engineering design, operational approaches, science objectives, and planned data products for REPT.