  In this partly expository paper we study van der Corput sets in $\Z^d$, with
a focus on connections with harmonic analysis and recurrence properties of
measure preserving dynamical systems. We prove multidimensional versions of
some classical results obtained for $d=1$ in \cite{K-MF} and \cite{R},
establish new characterizations, introduce and discuss some modifications of
van der Corput sets which correspond to various notions of recurrence, provide
numerous examples and formulate some natural open questions.
