We present observations of the young multiple system UX Tauri to look for circumstellar disks and for signs of dynamical interactions. We obtained SPHERE/IRDIS deep differential polarization images in the J and H bands. We also used ALMA archival CO data. Large extended spirals are well detected in scattered light coming out of the disk of UX Tau A. The southern spiral forms a bridge between UX Tau A and C. These spirals, including the bridge connecting the two stars, all have a CO (3–2) counterpart seen by ALMA. The disk of UX Tau C is detected in scattered light. It is much smaller than the disk of UX Tau A and has a major axis along a different position angle, suggesting a misalignment. We performed PHANTOM SPH hydrodynamical models to interpret the data. The scattered light spirals, CO emission spirals and velocity patterns of the rotating disks, and the compactness of the disk of UX Tau C all point to a scenario in which UX Tau A has been perturbed very recently (∼1000 years) by the close passage of UX Tau C.