Si--O and Al--O bonds are very strong, so that it may come as a surprise that aluminosilicates are riddled with structural phase transitions, particularly displacive transitions. For example, quartz (SiO2) has two extended phases, alpha and beta, and an incommensurate phase within a small temperature range between them. The feldspar series, (Na,K)AlSi3O8--CaAl2Si2O8, which is one of the most important geological materials, contains a number of different displacive and Al--Si site ordering phase transitions. These displacive phase transitions arise from the fact that aluminosilicates have framework structures, consisting of semi-rigid SiO4 and AlO4 tetrahedra and AlO6 octahedra, loosely jointed by shared oxygen atoms at a corner or along an edge. The force constants for deforming these units are typically an order of magnitude stronger than the weaker forces for rotating one unit about the other at the common corner or edge. It is therefore a good first approximation to take the units as completely rigid and the joints as completely free. The second step is to give the units a finite stiffness conveniently characterised by a single large stiffness constant S (strong) , and to include weak forces W between the units. The concept of ``rigid unit phonon modes'' (RUM) is constructed based on such structural observations. It gives a basis for understanding why phase transitions are found in many aluminosilicates, with the RUMs playing the role of the conventional soft mode. Indeed the units are so stiff that all these phase transitions would be quite impossible if they were not driven by unstable RUMs. Moreover the displacive instabilities are known to have a large role in driving atomic ordering, so that our model is relevant to those also. We expect that the basic ideas discussed here will also be important in aluminosilicate glasses, where the existence of RUMs (called floppy modes in the context of glasses) has been demonstrated. Technologically the most important application of these ideas might relate to the thermal expansion properties of glasses. We also expect that our ideas will have parallels for phase transitions in non-aluminosilicatecrystal systems.