This paper is a review of the results on the due date assignment and scheduling problems in the static deterministic case. In the problems under consideration, the objective is to find optimal values of the due dates and the related optimal schedule so that to minimize a given criterion based on the due dates and the completion times of jobs. 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 systems. According to the Just-In-Time concept jobs are to be completed neither too early nor too late which leads to the problems with non-regular measure of performance that includes earliness and tardiness costs. The due date assignment models where due dates depend on the jobs' processing times or on the positions of the jobs in the schedule are considered. The results on algorithms and complexity of the due date assignment and scheduling problems are summarized.