stantiated and quantified by applications of powerful methods coming from the field of disordered systems and the Anderson localization, most importantly by supermatrix approach due to Efetov  and its further adaptation to RMT by Weidenmueller, Verbaarschot, and Zirnbauer  ( see  for a few recent reviews). Also influential were a highly successful maximal-entropy based RMT approach to statistics of electronic transport in quantum-coherent (mesoscopic) samples introduced by Mello and collaborators , as well as the idea of parametric dependence of spectra of disordered and chaotic systems, and their RMT counterparts, developed by Simons and Altshuler  (see also related works  on statistics of level curvatures, as well as early papers  on ensembles interpolating between GOE and GUE and  on an impressively accurate verification of many aspects of RMT in acoustic waves experiments). Those and related developments resulted in a considerable broadening of the list of random matrix ensembles relevant to physical applications and amenable to analytical treatment beyond the classical Wigner-Dyson list. In particular, ensembles of random matrices which are not invariant with respect to changes of the basis attracted considerable attention, e.g. Band Random Matrices , which allowed for the effects of the Anderson localization to be correctly incorporated at the level of RMT. Moreover, the Dyson three-fold symmetry classification of underlying Hamiltonians was discovered to be insufficient for describing spectra appearing in Quantum Chromodynamics  as well as in disordered superconducting structures and was replaced by a more comprehensive list . Around the same time systematic investigations of non-Hermitian deformations of random matrix ensembles were undertaken due to their relevance for description of statistics of S-matrix poles (resonances) in quantum chaotic scattering  and in Quantum Chromodynamics with non-zero chemical potential , which also lead to a general boost of interest in their properties .
On the other hand, from a very different perspective deep connections to the Random Matrix Theory were discovered in the models of 2-dimensional Quantum Gravity . That line of research could be traced back to the t'Hooft's idea that in field theories with a large gauge group (as e.g. U(N)) the diagrammatic expansion will be dominated in the large-N limit by planar Feynman diagrams. In the RMT context such an expansion was first introduced in the influential paper by Brézin, Itzykson, Parisi and Zuber . Further developments showed that a method particularly suited to calculate the genus (or topological) expansion in 1/N turns out to be the loop equation method, see  and references therein. The ensuing links of random matrices to the theory of integrable systems, in particular, to Painleve transcendents and Toda/KdV hierarchies  and to diverse combinatorial problems  became an area of thriving activity.
Until the end of 1980's the research on properties of random matrices in Mathematics community was seemingly not as nearly as intensive as in Theoretical Physics. Among a few early mathematically rigorous and influential papers one could mention the works by Marcenko and Pastur describing the spectrum of large random covariance matrices , and by Arnold, Pastur, and Furedi & Komlos on various aspects of the eigenvalue distributions in ensembles of random matrices with independent entries . An important link of RMT to profound number-theoretical problems was provided by Montgomery  who revealed a certain similarity between eigenvalues of GUE/CUE matrices to those of zeroes of the Riemann zeta-function (Montgomery conjecture). On the other hand, needs of numerical analysis stimulated interests in the condition numbers of random matrices .
The situation changed considerably in 1990's after a few independent developments in various branches of Mathematics (among others, development of the "free probability" theory by D. Voiculescu and its relations to random matrices of infinite size ) lead to an essential boost of interest in various as