The present literature survey focuses on the stochastic economic lot scheduling problem (SELSP). The SELSP deals with the make-to-stock production of multiple standardized products on a single machine with limited capacity under random demands, possibly random setup times and possibly random production times. The main task of a production manager in this setting is the construction of a production plan for the machine. Based on the critical elements of such a production plan, we present a classification and extensive overview of the research on the SELSP together with an indication of open research areas. By doing so, we intend to stimulate the discussion on the important problems concerning the SELSP both from a theoretical and a practical point of view.