The nEDM apparatus at PSI has been used to search for different dark matter signatures utilizing its high sensitivity to shifts in the neutron precession frequency and its well-controlled low magnetic field at the μT level. Such a shift could be interpreted as a consequence of a short-range spin-dependent interaction that could possibly be mediated by axions or axion-like particles, or as an axion-induced oscillating electric dipole moment of the neutron. Another search, based on so-called UCN disappearance measurements, targeted previously reported signals of neutron to mirror-neutron oscillations. These dark matter searches confirmed and improved previous results, as detailed in this review.