This article reviews the microscopic origin of properties due to transition-metal (TM) impurities, M, in insulator materials. Particular attention is paid to the influence of pressure upon impurity properties. Basic concepts such as the electronic localization in an MX(N) complex, the electrostatic potential, V(R), arising from the rest of the lattice ions or the elastic coupling of the complex to the host lattice are initially exposed. The dependence of optical and magnetic parameters on the impurity-ligand distance, R, in cubic lattices is discussed in a first step. Emphasis is put on the actual origin of the R dependence of 10Dq. Examples revealing that laws for strict cubic symmetry cannot in general be transferred to lower symmetries are later given. This relevant fact is shown to come from allowed hybridizations like nd-(n+1)s as well as the influence of V(R). As a salient feature the different colour in ruby and emerald is stressed to arise from distinct V(R) potentials in Al(2)O(3) and Be(3)Si(6)Al(2)O(18). The last part of this review deals with electronic instabilities. The phenomena associated with the Jahn-Teller (JT) effect in cubic lattices, the origin of the energy barrier among equivalent minima and the existence of coherent tunnelling in systems like MgO:Cu(2+) are discussed. An increase of elastic coupling is pointed out to favour a transition from an elongated to a compressed equilibrium conformation. Interestingly the equilibrium geometry of JT ions in non-cubic lattices is shown to be controlled by mechanisms different to those in cubic systems, V(R) playing again a key role. The relevance of first principles calculations for clarifying the subtle mechanisms behind off-centre instabilities is also pointed out. Examples concern monovalent and divalent TM impurities in lattices with the CaF(2) structure. The instability due to the transition from the ground to an excited state is finally considered. For complexes with significant elastic coupling vibrational frequencies and the Stokes shift are expected to undergo bigger changes through a chemical rather than a hydrostatic pressure. The reduction of Huang-Rhys factors upon increasing the pressure is discussed as well.