High pressure has been one of key tools for discovering and accessing new phases and novel properties of materials. Under these extreme conditions, it is possible to obtain information about the structural instabilities and to probe the delicate balance between short and long range interactions, which is fundamental for understanding the emergence of many properties. In this paper we reviewed the high-pressure behavior of some molybdate and tungstate materials, which comprises a large class of inorganic compounds that exhibit interesting physical properties (optical, ferroelastic, ferroelectric, negative thermal expansion) and have technological applications in different fields. These materials have a rich polymorphism in high pressures and some of them exhibit pressure-induced amorphization, thus making molybdates and tungstates compounds good prototypes to exploit new concepts about the physics of amorphization processes and about chemical decomposition under high pressure. We discussed how the combination of short and long-range probe techniques (which gives detailed information on the structural changes occurring in these materials) under high-pressures provides significant insight into the origin of lattice instabilities and pressure-induced amorphization in this particular class of inorganic materials. Furthermore, we reviewed in detail, how these structural changes affect their optical and ferroelectric properties. The conclusions derived from the high-pressure studies duly reviewed herewith have important implications for science and applications of these materials. (C) 2012 Elsevier Ltd. All rights reserved.