A point-scanning luminescent microscope, especially for studying biological objects, has at least one collimated light source for producing an excitation light beam, an optical arrangement which focuses the light of the excitation light source on an object to be studied, at least one detector arrangement for acquiring light emitted by the object, an optical arrangement which collects the light emitted by the object and supplies it to the detector arrangement, and a scanner arrangement which causes relative movement between the scanning light beam and the object in at least two directions. The scanner arrangement has piezoactuators for achieving scanning movements between the scanning light beam and object. The detector arrangement can have a surface sensor which forms a confocal diaphragm. The light source can be designed to deliver rectangular pulses. When the microscope is designed for twin-photon fluorescent microscopy, an objective lens is provided for illuminating the object and can be is used, at the same time, for collecting some of the photons emitted by the object, and a second detector is provided behind a condenser lens of the objective lens.