Passivity and dissipativity have proven to be useful analysis and design tools in nonlinear systems. We generalize notions of passivity and dissipativity to fractional order systems. Besides reducing to existing concepts when the order of the system is an integer, our proposed definitions guarantee two additional properties that passive integer order systems have. First, we show that similar to dissipative integer order systems, a QSR dissipative fractional order system is also L-2 stable. Second, under fairly weak conditions, we show that passive and strictly passive fractional order systems are also stable in the sense of Lyapunov and Mittag-Leffler, respectively. Third, we show that passive fractional order systems satisfy compositionality properties; specifically, parallel and feedback interconnection of passive fractional order systems are also passive. Having provided these definitions and analyzed their properties, we study the problem of passivating a fractional order system by designing a feedback controller such that the closed-loop system is passive. Finally, we illustrate the proposed concepts through numerical examples.