Dielectric resonator antenna (DRA) has been proposed recently as a viable new way to build antenna in view of some of the advantages they offer. One recent trend in DRA research focuses on using composite and hybrid structures. Some considerable investigations are already underway showing quite interesting and significant features. A brief review of the topic is presented in this article. A general discussion comparing a microstrip patch and a DRA is provided in the beginning. Some state-of-the-art developments and associated challenges in the DRA design and applications are also discussed.