Fiber-reinforced concrete (FRC) is increasingly used in structural applications owing to its benefits in terms of toughness, durability, ductility, construction cost and time. However, research on the creep behavior of FRC has not kept pace with other areas such as short-term properties. Therefore, this study aims to present a comprehensive and critical review of literature on the creep properties and behavior of FRC with recommendations for future research. A transparent literature search and filtering methodology were used to identify studies regarding creep on the single fiber level, FRC material level, and level of structural behavior of FRC members. Both experimental and theoretical research are analyzed. The results of the review show that, at the single fiber level, pull-out creep should be considered for steel fiber-reinforced concrete, whereas fiber creep can be a governing design parameter in the case of polymeric fiber reinforced concrete subjected to permanent tensile stresses incompatible with the mechanical time-dependent performance of the fiber. On the material level of FRC, a wide variety of test parameters still hinders the formulation of comprehensive constitutive models that allow proper consideration of the creep in the design of FRC elements. Although significant research remains to be carried out, the experience gained so far confirms that both steel and polymeric fibers can be used as concrete reinforcement provided certain limitations in terms of structural applications are imposed. Finally, by providing recommendations for future research, this study aims to contribute to code development and industry uptake of structural FRC applications.