Random matrix theory is a very broad and well-developed research area at the intersection of physics, statistics, probability and combinatorics (and arguably others). Applications range from numerical analysis to engineering, to biology, economics, signal processing and machine learning. Classically, the type of matrices that have been studied have certain invariance properties (e.g., orthogonal), and therefore are mostly dense; however, the last decade has been marked by a tremendous increase in sparse applications, particularly related to the ubiquity of sparse networks and graphs. This, in turn, has led to rapid development of sparse random matrix theory. Some spectral properties (eigenstatistics) of sparse matrices turn out to match the dense ones, but others generate new and interesting phenomena. I will provide a high-level perspective on this rapidly evolving field, and describe some applications of interest.