COrE+ has been proposed to ESA as a medium-class mission for investigating, within the framework of the ESA Cosmic Vision program, a set of important scientific questions that require high sensitivity, full-sky observations of the sky emission at wavelengths ranging from millimeter-wave to the far-infrared. Its main scientific objective is to explore the physics of inflation and the distant universe, probing cosmic history from very early times until now as well as the structures, distribution of matter, and velocity flows throughout our Hubble volume. COrE+ will survey the full sky in 19 frequency bands in both intensity and polarization, from 60 to 600 GHz.