Abstract：It plays an important role in geometry and topology of manifolds to study sphere theorems. During the past fifteen years, a number of great achievements on sphere theorems, including the Poincare conjecture, the 1/4-pinching differentiable sphere theorem, and the Willmore conjecture, have been made by several geometers. In this talk, I will discuss recent progress and new techniques developed in the study of sphere theorems. I will also propose some open problems in this area.