In this talk, we discuss some results on compactness of
(iterated) commutators of singular integral operators. These
operators include the Cauchy integraloperator, Beurling-Ahlforstransform, Riesz transform and so on. We also consider the application to the study of Beltrami equation. This work is
joint with Weichao Guo, Jianxun He, Jin tao, Huoxiong Wu and Dachun Yang.