In 1926, Hopf showed that every compact, simply connected manifold with constant curvature 1 is isometric to the standard round sphere. Motivated by this result, Hopf posed the question whether a compact, simply connected manifold with sufficiently pinched curvatured must be a sphere topologically. This question has been studied by many authors during the past decades, a milestone being the topological sphere theorem of Berger and Klingenberg. I will discuss the history of this problem and sketch the proof of the Differentiable Sphere Theorem. The proof relies on the Ricci flow
method pioneered by Richard Hamilton.