Historiography has pointed out that the time between the mid 1910s and the early 1930s can be considered a pivotal period in the history of stellar astrophysics. In those years, scholars like Saha and Eddington first applied atomic physics to astrophysics. Theoretical astrophysics was born. This led to the development of the first physically sound models for stellar interiors and atmospheres. These landmark achievements spurred scholars to elaborate theories for stellar evolutions, and in the following decades several astrophysicists focused on (...) this problem. The evolutionary role of red giants turned out to be the main issue. Those stars were initially assumed to be young ones going through the formation stage, but astrophysicists gradually realized that they were rather to be considered old, evolved stars. The solution of the giant stars issue required a couple of decades: it was not until the mid 1950s that a satisfactory explanation was obtained. This provides a detailed picture of the theories of stellar evolution from the 1930s to the 1950s and of the solution to the red giants problem, with special emphasis on how such a solution was made possible by a series of subsequent steps: the identification of changing chemical composition as a main evolutionary feature of a star, the inclusion of nuclear physics within the theoretical framework of stellar astrophysics, the recognition of the importance of inhomogeneities that settle within stars as nuclear processes go on. (shrink)