In this paper, we present several applications of recent results of large random matrix theory (RMT) to the performance analysis of small cell networks (SCNs). In a nutshell, SCNs are based on the idea of a very dense deployment of low-cost low-power base stations (BSs) that are substantially smaller than existing macro cell equipment. However, a massive network densification causes many new challenges to the optimal system design, such as interference and mobility management, self-organization, security, coverage and performance prediction. We focus especially on the last point and show how RMT can be used to provide tight and tractable approximations of key performance parameters, such as capacity and outage probability, and demonstrate how it can be applied to related optimization problems. Although the results are only tight in the large system limit, they yield close approximations for small systems with as little as three transmitters and receivers. Thus, we believe that RMT offers many yet unexplored applications to the study of SCNs and hope that this paper stimulates further research in this direction.