Summary. We present a survey about weights for one-sided operators, one of the areas in which Carlos Segovia made significant contributions. The classical DunfordSchwartz ergodic theorem can be considered as the first result about weights for the one-sided Hardy-Littlewood maximal operator. From this starting point, we study weighted inequalities for one-sided operators: positive operators like the Hardy averaging operator, the one-sided Hardy-Littlewood maximal operator, singular approximations of the identity, one-sided singular integrals. We end with applications to ergodic theory and with some recent results in dimensions greater than 1.
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