, 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 aspects of the Random Matrix Theory. First of all, the wealth of information obtained by heuristic methods of theoretical physics called for a proper understanding by mathematical standards. To that end, considerable efforts were directed towards proving conjectured universality  of correlations between eigenvalues of random matrices beyond classical (Gaussian or Circular) Wigner-Dyson ensembles, that is independence of their properties of the choice of the distribution of matrix elements for general RMT ensembles in the limit of large dimension. First, such a universality was verified for a rather general class of invariant ensembles , the line of research resulting, in particular, in development of the powerful Riemann-Hilbert approach to the asymptotics of orthogonal polynomials . More recently similar universality was extended also to a broad class of ensembles with independent, identically distributed entries . Deserve mentioning also works  on the large deviation statistics of spectral measure and on distribution of the number of eigenvalues in a given interval of spectrum, as well as the paper  which nontrivially extends the Dyson work on Brownian motion of eigenvalues by relating it to non-intersecting random walks.
Around the same time the statistics of the largest eigenvalue in Gaussian Ensembles attracted considerable attention . Its probability density first derived by C. Tracy and H. Widom  appeared to be highly universal  and emerged in such important combinatorial problems as the distribution of the length of the longest increasing subsequence of random permutations  as well as in applications in statistical mechanics: statistics of the height of random surfaces obtained by polynuclear growth  and the lowest energy state as well as the free energy of a directed polymer in random environment . Yet another highly influential development followed the works by Keating and Snaith  in providing powerful evidences in favour of a very intimate connection between the properties of characteristic polynomials o