We first review advances in rescheduling, traditionally viewed as an approach to tackle uncertainty, including methods that rely on recourse through feedback as well as methods that account for uncertainty a priori. Then, we show that traditional event-triggered rescheduling has some shortcomings which can be addressed if rescheduling is approached as an online problem. We review methods that consider aspects of this online problem and define notation and some key features of this problem. Furthermore, we propose a broad framework for the classification of online scheduling methods. Finally, we discuss a number of open research questions, including the generation of high quality of closed-loop (implemented) schedules through the selection of appropriate model, horizon length, time-step, objective function modifications, and constraint addition. (C) 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.