An analysis and review of the basic problems associated with the efficient operation of production and assembly lines, and the evaluation of the effectiveness of internal storage. Three basic approaches are discussed: loss transfer (fractions of losses due to stoppage are transferred to succeeding stages) stochastic (distribution of durations of working and down states of each stage leading to determination of state probabilities) queue (treating production lines or queue systems with limitations on size of queue between stages) The concept of the cyclic queue is reviewed and discussed in production line terms (i.e., following a frame or jig through its cycles). The approaches are compared and industrial illustrations are given. The methods discussed apply to problems which, in physical appearance, are different from production lines; among these are chemical production, overhaul and repair systems, etc. A review of the field indicates that considerably more research and analysis is required.