We review recent progress in applying the theory of rigidity to glassy networks and to proteins. These three dimensional systems require a generalization of Laman's theorem, which we have used to develop a technique called the Pebble Game which allows the rigid regions (containing both isostatic and overconstrained parts) and the flexible joints between them, to be found. We show that a flexibility index, which measures the local density of floppy modes, is useful in characterizing the network. A sampling of recent results is given for network glasses, where we show how the glass structure can self-organize to produce an intermediate phase that is stress-free and contains a percolating isostatic cluster. In proteins, we show how maps of the rigid regions and flexible joints, as well as maps of the flexibility index, can help to elucidate the connection between structure and function.
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