Eclipses and problems related to them have been, from ancient times, one of the main interests not only of astronomers but indeed of all mankind. The appearance of eclipses, lunar as well as solar, excited the imagination of our ancestors and provoked their curiosity to explain their origin or to use them for the further investigation of celestial bodies. With the present development of astronomy the eclipse problems are not limited to the Sun and the Moon, as in the past, but have been progressively extended to the components of the solar system and to domains of radiations other than optical ones. Our intention is to give an account of all these problems in their theoretical and experimental form with some additions on their historical development. Those of our readers not interested in the historical side may feel at first inclined to ignore this part, but we are sure that eventually they will be sufficiently interested to repair this omission.