The combined increase of energy demand and environmental pollution at a global scale is forcing a rethinking of energy supply policies and production models in sustainable terms. In order to flatten demand peaks in power plants, energy suppliers adopted pricing policies that stimulate a change in the consumption practices of customers. One example of such policies is the Time-of-Use (TOU)-based tariffs, which encourage electricity usage at off-peak hours by means of low prices, while penalizing peak hours with higher prices. To avoid a sharp rise of the energy supply costs, manufacturing industry must carefully reschedule the production processes, by shifting them towards less expensive periods. TOU-based tariffs impose specific constraints on the completions of the jobs involved in the production processes as well as a partitioning of the time horizon of the production into a set of time slots, whose associated non-negative cost become part of the objective to be optimized. In this article, we review the flourishing literature on job scheduling in presence of TOU-based energy tariffs, with the view to provide researchers and practitioners with a framework that may guide them towards the most important theoretical results on the topic as well as the most prominent practical applications in sustainable manufacturing.