Driven by a wide range of applications, high-dimensional statistical inference has seen
significant developments over the last few years. These and other related problems have also
attracted much interest in a number of fields including applied mathematics, engineering,
and statistics. In this talk I will discuss some recent advances on several problems in
high-dimensional inference including compressed sensing, low-rank matrix recovery, and
estimation of large covariance matrices. The connections as well as differences among these
problems will be also discussed.