A detailed comparison is made between the predictions of stellar evolution calculations and the observations of red giants in old open clusters. Colour- magnitude diagrams are presented for several such clusters, in which relative proper motions have been used to eliminate non-members. The published observations of other old clusters are suinmarized. A prominent feature of all these clusters is a' clump `of red giants, centred near Mv = + I, B-V = +i.o, which is tentatively identified with the horizontal branch found in globular clusters. Comparison with various theoretical calculations, mostly by I. Iben and J. Faulkner, supports this identification and indicates that the stars have a helium-burning core surrounded by a hydrogen-burning shell. The near constancy of the absolute magnitude of the clump is then interpreted as observational evidence for the occurrence of electron degeneracy in the cores of low mass red giants. The use of the clump for crude determinations of cluster distances and reddening, and as evidence of the internal composition of the stars, is advocated. Finally, it is suggested that a large number of field red giants may be in the helium-burning phase of evolution some of which may be used to investigate mass loss and internal mixing in evolving stars.