Elasticity in circuits and systems provides tolerance to variations in computation and communication delays. This paper presents a comprehensive overview of elastic circuits for those designers who are mainly familiar with synchronous design. Elasticity can be implemented both synchronously and asynchronously, although it was traditionally more often associated with asynchronous circuits. This paper shows that synchronous and asynchronous elastic circuits can be designed, analyzed, and optimized using similar techniques. Thus, choices between synchronous and asynchronous implementations are localized and deferred until late in the design process.