While the modern computer technology is widely applied, the large dimensional data analysis has been becoming more and more important and attracted consid erable attention of statisticians.Both real applications and theoretical investiga tion have demonstrated that the traditional statistical procedures developed by the classical limiting theorems (i.e.those as sample sizes tending to infinity while the dimension is fixed) will induce intolerable errors when the dimension of data is large.Therefore, there is an urgent need to develop new limiting theorems and statistical procedures for dealing with large dimensional data.Up to latest, except for some ad hoc approaches,the only systematic limiting theory which can bc applied to large dimensional data analysis is the random matrix theory RMT).Therefore,the RMT has received more and more attention of statisticians and users in other applied disciplines.In this talk, I shall briefly introduce some basic concepts and some important results in RMT as well as some unsolved problems.