Framework materials have structures containing strongly bonded polyhedral groups of atoms connected through their vertices. Typically the energy cost for variations of the inter-polyhedral geometry is much less than the cost of distortions of the polyhedra themselves - as in the case of silicates, where the geometry of the SiO4 tetrahedral group is much more strongly constrained than the Si-O-Si bridging angle. As a result, framework materials frequently display intrinsic flexibility, and their dynamic and static properties are strongly influenced by low-energy collective motions of the polyhedra. Insight into these motions can be obtained in reciprocal space through the `rigid unit mode' (RUM) model, and in real-space through template-based geometric simulations. We briefly review the framework flexibility phenomena in energy-relevant materials, including ionic conductors, perovskites and zeolites. In particular we examine the `flexibility window' phenomenon in zeolites and present novel results on the flexibility window of the EMT framework, which shed light on the role of structure-directing agents. Our key finding is that the crown ether, despite its steric bulk, does not limit the geometric flexibility of the framework.