  We study the notion of recurrence and some of its variations for linear
operators acting on Banach spaces. We characterize recurrence for several
classes of linear operators such as weighted shifts, composition operators and
multiplication operators on classical Banach spaces. We show that on separable
complex Hilbert spaces the study of recurrent operators reduces, in many cases,
to the study of unitary operators. Finally, we study the notion of product
recurrence and state some relevant open questions.
