Queues (or waiting lines) help facilities or businesses provide service in an orderly fashion. Forming a queue being a social phenomenon, it is beneficial to the society if it can be managed so that both the unit that waits and the one that serves get the most benefit. For instance, there was a time when in airline terminals passengers formed separate queues in front of check-in counters. But now we see invariably only one line feeding into several counters. This is the result of the realization that a single line policy serves better for the passengers as well as the airline management. Such a conclusion has come from analyzing the mode by which a queue is formed and the service is provided. The analysis is based on building a mathematical model representing the process of arrival of passengers who join the queue, the rules by which they are allowed into service, and the time it takes to serve the passengers. Queueing theory embodies the full gamut of such models covering all perceivable systems which incorporate characteristics of a queue. This chapter introduces basic elements of queueing systems and problems we face in analyzing item. A historical perspective is provided to understand the significance of the subjects.