[en] Solar Orbiter will for the first time study the Sun with a full suite of in-situ and remote sensing instruments from inside 0.25 AU and will provide imaging and spectral observations of the Sun’s polar regions, from out of the ecliptic. This proximity to the Sun will also have the significant advantage that the spacecraft will fly in near synchronization with the Sun’s rotation, allowing observations of the solar surface and heliosphere to be studied from a near co-rotating vantage point for almost a complete solar rotation. The mission’s ambitious characteristics draw severe constraints on the design of these instruments. The scientific objectives of Solar Orbiter rely ubiquitously on the Extreme EUV Imager suite (EUI). The EUI instrument suite on board of Solar Orbiter is composed of two high resolution imagers (HRI), one at Lyman α and one dual band at the two 174 and 335 EUV passbands in the extreme UV, and one dual band full-sun imager (FSI) working alternatively at the two 174 and 304 EUV passbands. In all the units, the image is produced by a mirror-telescope, working in nearly normal incidence. The EUV reflectivity of the optical surfaces is obtained with specific EUV multilayered coatings, providing the spectral selection of the EUV units (1HRI and 1 FSI). The spectral selection is complemented with very thin filters rejecting the visible and IR radiation. Due to its orbit, EUI / Solar Orbiter will see 20 solar constants and an entrance baffle to limit the solar heat input into EUI is needed. The paper presents the scientific objectives of EUI and also covers the EUI instrument development plan which will require some trade-off between existing and promising technologies.