As a promising technology in beyond-5G (B5G) and 6G, dual-function radar-communication (DFRC) aims to ensure both radar sensing and communication on a single integrated platform with unified signaling schemes. To achieve accurate sensing and reliable communication, large-scale arrays are anticipated to be implemented in such systems, which brings out the prominent issues on hardware cost and power consumption. To address these issues, hybrid beamforming (HBF), beyond its successful deployment in communication-only systems, could be a promising approach in the emerging DFRC ones. In this article, we investigate the development of the HBF techniques on the DFRC system in a self-contained manner. Specifically, we first introduce the basics of the HBF based DFRC system, where the system model and different receive modes are discussed with focus. Then we illustrate the corresponding design principles, which span from the performance metrics and optimization formulations to the design approaches and our preliminary results. Finally, potential extension and key research opportunities, such as the combination with the reconfigurable intelligent surface, are discussed concisely.