Fundamental physics with ultracold neutrons

We review recent proposals for the use of ultracold neutrons (UCN) in improved experiments: one measuring the neutron lifetime for beta-decay, and the other searching for a permanent electric dipole moment of the neutron. In connection with beta-decay we discuss the old question whether the time dependence of decay should be purely exponential, as commonly assumed, or whether it should exhibit the deviations from exponential behaviour predicted by quantum mechanics. Finally, we point out several 'anomalies' reported over the years in storage and diffraction experiments with ultracold neutrons, none of which seems to have found a satisfactory explanation so far. (author)