In this paper, we aim at providing a unified framework of the common due date assignment and scheduling problems in the deterministic case by surveying the literature concerning the models involving single machine and parallel machines. We focus on static production settings in which a fixed set of is available for processing as opposed to dynamic production settings where jobs continuously arrive in the system and should be scheduled on-line. The problems with due date determination have received considerable attention in the last ten years due to the introduction of new methods of inventory management such as Just-In-Time (JIT) systems. The common due date model which is also known in scheduling literature as CON model, where CON stands for constant flow allowance, corresponds, for instance, to an assembly system in which the components of the product should be ready at the same time, or to a shop where several jobs constitute a single customer's order. In the problems under consideration, the objective is to find an optimal value of the common due date and the related optimal schedule in order to optimize a given criterion based on the due date and the completion times of jobs. The results on the algorithms and complexity of the common due date assignment and scheduling problems are summarized.