Change detection (CD) methods have been applied to optical data for decades, while the use of hyperspectral data with a fine spectral resolution has been rarely explored. CD is applied in several sectors, such as environmental monitoring and disaster management. Thanks to the PRecursore IperSpettrale della Missione operativA (PRISMA), hyperspectral-from-space CD is now possible. In this work, we apply standard and deep-learning (DL) CD methods to different targets, from natural to urban areas. We propose a pipeline starting from coregistration, followed by CD with a full-spectrum algorithm and by a DL network developed for optical data. We find that changes in vegetation and built environments are well captured. The spectral information is valuable to identify subtle changes and the DL methods are less affected by noise compared to the statistical method, but atmospheric effects and the lack of reliable ground truth represent a major challenge to hyperspectral CD.