We study boundedness of commutators of singular integrals in connection with different types of John-Nirenberg spaces of bounded mean oscillation (BMO), which plays an important role in singular integral theory. It is a classical result of Coifman, Rochberg, and Weiss that function $b$ is in BMO, if and only if the commutator of $b$ and a Riesz transform $R_j$ is bounded on $L^p$, where the commutator is defined as $[b,R_j]=b R_j-R_j b$ and $b$ is understood as a pointwise multiplication operator. We will discuss several recent results along this line, including the discovery of a new class of BMO spaces in the multi-parameter setting, which are characterized by the boundedness of certain commutators. The main tool that is involved is a representation of arbitrary singular integrals as averages of simpler components, one of the most powerful tools that have emerged in the last fifteen years of singular integral theory.