This article presents a brief survey of two-sided matching. We introduce the reader to the problem of two-sided matching in the context of the college admission model and explain two central requirements for a matching mechanism: stability and non-manipulability. We show how the frequently used ‘Boston Mechanism’ fails these key requirements and describe how an alternative, the Deferred Acceptance Algorithm, leads to stable matchings but fails to be non-manipulable in general. A third mechanism, the Top Trading Cycle, is efficient and non-manipulable when only one side of the match acts strategically. We also discuss some applications of matching theory.