Production planning problems have been formulated and solved as optimization problems since the early 1950s, and an extensive literature has been developed. The widespread use of Enterprise Resource Planning systems and developments in information technology and scientific computing have opened the way for even wider use of these techniques in industry. In this chapter, we review the basic formulations that have been the mainstay of academic research and industrial practice for the last five decades, assess their strengths and weaknesses, and discuss a number of interesting new directions that have emerged recently. We especially focus on models that support decisions on production volumes and order release over time and highlight the related issues on determining planned lead times.