In this talk, I will discuss the commutator of Cauchy type integrals $\mathcal C$ on a bounded strongly pseudoconvex domain $D$ in $\mathbb C^n$ with boundary $bD$ satisfying the minimum regularity condition $C^{2}$ as in the recent result of Lanzani-Stein. We point out that in this setting the Cauchy type integrals $\mathcal C$ is the sum of the essential part $\mathcal C^\sharp$ which is a Calderon-Zygmund operator and a remainder $\mathcal R$ which is no longer a Calderon-Zygmund operator. We show that the commutator $[b, \mathcal C]$ is bounded on $L^p(bD)$ ($p>1$) if and only if $b$ is in the BMO space on $bD$. Moreover, the commutator $[b, \mathcal C]$ is compact on $L^p(bD)$ ($p>1$) if and only if $b$ is in the VMO space on $bD$. Our method can also be applied to the commutator of Cauchy-Leray integral in a bounded, strongly $\mathbb C$-linearly convex domain $D$ in $\mathbb C^n$ with the boundary $bD$ satisfying the minimum regularity $C^{1,1}$. Such a Cauchy-Leray integral is a Calderon-Zygmund operator as proved in the recent result of Lanzani-Stein. This method provides another proof of the boundedness and compactness of commutator of Cauchy-Szego operator on a bounded strongly pseudoconvex domain $D$ in $\mathbb C^n$ with smooth boundary, firstly established by Krantz-Li.This is a joint work with X. T. Duong, J. Li, M. Lacey and B. D. Wick.