<p>The integrated problem, where scheduling production activities and maintenance actions are considered in one model, has attracted attention of researchers in recent years. In this paper, we present a literature review of papers dealing with integrated models on single-machine problem. The motivation of this paper comes from the fact that there is no recent published review focusing on the integrated production and maintenance problem on single machine. In the existing surveys, only scheduling with unavailability constraints was considered. However, we aim to consider in addition new models where preventive maintenance action numbers and dates are decision variables. To well describe all the surveyed problems, we use and adapt the Graham’s notation. The computational complexity and the proposed solution algorithms are given for each surveyed problem. Studied models are classified according to predefined maintenance data into: scheduling with deterministic availability constraint, scheduling with flexible availability constraint, scheduling with limited number of unavailability periods and joint production and preventive maintenance problems. We analyze each of the four classes of problems. We conclude our paper with future research directions.</p>