EMU is a wide-field radio continuum survey planned for the new Australian Square Kilometre Array Pathfinder (ASKAP) telescope. The primary goal of EMU is to make a deep (rms ∼ 10 μJy/beam) radio continuum survey of the entire Southern sky at 1.3 GHz, extending as far North as +30° declination, with a resolution of 10 arcsec. EMU is expected to detect and catalogue about 70 million galaxies, including typical star-forming galaxies up to z ∼ 1, powerful starbursts to even greater redshifts, and active galactic nuclei to the edge of the visible Universe. It will undoubtedly discover new classes of object. This paper defines the science goals and parameters of the survey, and describes the development of techniques necessary to maximise the science return from EMU.