  We present the theory of Cauchy-Fantappi\'e integral operators, with emphasis
on the situation when the domain of integration, $D$, has minimal boundary
regularity. Among these operators we focus on those that are more closely
related to the classical Cauchy integral for a planar domain, whose kernel is a
holomorphic function of the parameter $z\in D$. The goal is to prove $L^p$
estimates for these operators and, as a consequence, to obtain $L^p$ estimates
for the canonical Cauchy-Szeg\"o and Bergman projection operators (which are
not of Cauchy-Fantappi\'e type).
