  This is an expository paper on the characterization of the even (or odd)
smooth homogeneous convolution Calder\'on-Zygmund operators in R^n such that
the maximal singular integral can be controlled in the L^2 norm by the singular
integral. We focuss attention on special cases of the general statements to
convey the main ideas of the proofs in a transparent way, as free as possible
of the technical complications inherent to the general case. Particular
attention is devoted to higher Riesz transforms. The exposition is based on two
papers by J.Mateu, J.Orobitg, C.P\'erez and J.Verdera published in 2010 and
2011.
