Condition-based maintenance (CBM) is a maintenance strategy that collects and assesses real-time information, and recommends maintenance decisions based on the current condition of the system. In recent decades, research on CBM has been rapidly growing due to the rapid development of computer-based monitoring technologies. Research studies have proven that CBM, if planned properly, can be effective in improving equipment reliability at reduced costs. This paper presents a review of CBM literature with emphasis on mathematical modeling and optimization approaches. We focus this review on important aspects of the CBM, such as optimization criteria, inspection frequency, maintenance degree, solution methodology, etc. Since the modeling choice for the stochastic deterioration process greatly influences CBM strategy decisions, this review classifies the literature on CBM models based on the underlying deterioration processes, namely discrete- and continuous-state deterioration, and proportional hazard model. CBM models for multi-unit systems are also reviewed in this paper. This paper provides useful references for CBM management professionals and researchers working on CBM modeling and optimization. •A review on Condition-based maintenance (CBM) optimization models is presented.•The CBM models are classified based on the underlying deterioration processes.•Existing CBM models for both single- and multi-unit systems are reviewed.•Future essential research directions on CBM are identified.