This contribution summarizes recent work in the field of lot sizing and scheduling. The objective is not to give a comprehensive literature survey, but to explain differences of formal models and to provide some first readings recommendations. Our focus is on capacitated, dynamic, and deterministic cases. To underscore the importance of the research efforts, current practice is described and its shortcomings are exposed. Mathematical programming models where the planning horizon is subdivided into several discrete periods are given for both approaches that are well-established and approaches which may represent tomorrow's state of the art. Two research directions are discussed in more detail: continuous time models and multi-level lot sizing and scheduling. The paper concludes with some advice for future research activities.