Hyperspectral imaging aims at providing information on both the spatial and the spectral distribution of light, with high resolution. However, state-of-the-art protocols are characterized by an intrinsic trade-off imposing to sacrifice either resolution or image acquisition speed. We address this limitation by exploiting light intensity correlations, which are shown to enable overcoming the typical downsides of traditional hyperspectral imaging techniques, both scanning and snapshot. The proposed approach also opens possibilities that are not otherwise achievable, such as sharper imaging and natural filtering of broadband spectral components that would otherwise hide the spectrum of interest. The enabled combination of high spatial and spectral resolution, high speed, and insensitivity to undesired spectral features shall lead to a paradigm change in hyperspectral imaging devices and open up new application scenarios. Published by the American Physical Society 2024