Hybrid Rocket Engines (HREs) generate thrust by combining a liquid and a solid propellant. Given the hybrid nature, HREs possess several advantages over Liquid Rocket Engines (LREs) and Solid Rocket Motors (SRMs). Hybrid engines are cheaper and less complex than LREs while being safer and more sustainable than SRMs. HREs are throttleable as well as re-ignitable and their theoretical achievable specific impulses (Isp) lie between SRMs and LREs. However, hybrid engines suffer from several disadvantages that refrained them from reaching their full potential yet. Among other drawbacks, HREs have a low maturity, high fuel residuals and a low solid fuel regression rate. In fact, the low regression rate is considered the limiting characteristic for HRE applications. Around the globe, great research effort is put into enhancing the regression rate. Summarizing, the authors group the techniques together as a) adjusting the solid fuel properties, b) advanced injection methods and designs and c) improving the combustion chamber design. Each of these techniques comes with a different set of advantages and drawbacks, which need to be considered when designing a HRE.