The derived category of coherent sheaves on projective varieties is a fundamental object in algebraic geometry. This talk is mainly concerned with the problem of description for varieties, which have equivalent derived categories of coherent sheaves. I will talk about the concept of derived equivalence, Fourier-Mukai transform and a lot of beautiful results of Orlov and Huybrechts on derived Torelli theorem over complex numbers. At last, I will also mention our recent progress for such problem over positive characteristic fields.