The due date assignment and scheduling problems arise in production planning when the management is faced with setting realistic due dates for a number of jobs. Most research on scheduling with due date assignment is focused on optimal sequencing of independent jobs. However, it is often found in practice that some products are manufactured in a certain order implied, for example, by technological, marketing or assembly requirements and this can be modeled by imposing precedence constraints on the set of jobs. In classical deterministic scheduling models, the processing conditions, including job processing times, are usually viewed as given constants. However, in many real-life situations, the processing conditions may vary over time, thereby affecting actual durations of jobs. There are two categories of scheduling models in which the actual processing time of a job depends on its place in the schedule: in scheduling with deterioration, the later a job starts, the longer it takes to process, and in scheduling with learning, the actual processing time of a job gets shorter, provided that the job is scheduled later. We review the results on scheduling with due date assignment under such conditions on job processing as given precedence constraints or various scenarios of processing time deterioration and learning.