Large amounts of invisible matter have been discovered back in 1933when the Swiss astronomer Fritz Zwicky measured for the first timethe velocity dispersion of individual galaxies inside the Coma cluster.Since then, this pioneering observation has been confirmed on scalesranging from galactic radii to cosmological distances. The existenceof the so–called astronomical dark matter is now well established.The puzzle lies in the fact that this essential component of the universeis not made of ordinary atoms and electrons. The astronomical dark matteris indeed non–baryonic. Its nature is still an unresolved issue. Manytheoretical ideas and proposals have flourished in the past thirty yearsand yet none of them provides a definite answer.I have the challenging task to introduce the cohort of these dark mattercandidates to you. They make up a bestiary of exotic species which havebeen recently proliferating. Instead of a liste à la Prévert,I will present a tentative classification of the various models.