Hybrid rocket engines are promising propulsion systems which present appealing features such as safety, low cost, and environmental friendliness. On the other hand, certain issues hamper the development hoped for. The present paper discusses approaches addressing improvements to one of the most important among these issues: low fuel regression rate. To highlight the consequence of such an issue and to better understand the concepts proposed, fundamentals are summarized. Two approaches are presented (multiport grain and high mixture ratio) which aim at reducing negative effects without enhancing regression rate. Furthermore, fuel material changes and nonconventional geometries of grain and/or injector are presented as methods to increase fuel regression rate. Although most of these approaches are still at the laboratory or concept scale, many of them are promising.