Corona problem was initiated from function algebra, then it became one of the most important problems in harmonic analysis and complex analysis. For the case of one complex variable, the problem was solved by L. Carleson in 1960s. In the several complex variables, the problem remains open. In this talk, I will introduce the development of the Corona Problems of one and several complex variables. I will also introduce the Hormander’s weighted L2-estimate for ∂, and demonstrate how to use the weighted L2 estimates to prove some old and new results on Corona Problem.