Some problems of the optics of ultracold neutrons (UCNs) are examined. The possibility is discussed of designing high-resolution neutron-optical systems, and in particular, a neutron microscope using UCNs. The problems are analyzed of the specific distortions involving the appreciable action on the motion of UCNs of the Earth's gravitational forces. Experiments on focusing of neutrons are reviewed, the methods of designing neutron-optical systems for UCNs are presented, and the existing neutron-microscope projects are described.