We present the concept of BlueMUSE, a blue-optimised, medium spectral resolution, panoramic integral field spectrograph based on the MUSE concept and proposed for the Very Large Telescope. With an optimised transmission down to 350 nm, a larger FoV (1.4 x 1.4 arcmin2) and a higher spectral resolution compared to MUSE, BlueMUSE will open up a new range of galactic and extragalactic science cases allowed by its specific capabilities, beyond those possible with MUSE. For example a survey of massive stars in our galaxy and the Local Group will increase the known population of massive stars by a factor >100, to answer key questions about their evolution. Deep field observations with BlueMUSE will also significantly increase samples of Lyman-alpha emitters, spanning the era of Cosmic Noon. This will revolutionise the study of the distant Universe: allowing the intergalactic medium to be detected unambiguously in emission, enabling the study of the exchange of baryons between galaxies and their surroundings. By 2030, at a time when the focus of most of the new large facilities (ELT, JWST) will be on the infra-red, BlueMUSE will be a unique facility, outperforming any ELT instrument in the Blue/UV. It will have a strong synergy with ELT, JWST as well as ALMA, SKA, Euclid and Athena.