The addition of fibers to strengthen recycled concrete can strengthen the inherent deficits and deficiencies of concrete containing recycled aggregates to some extent and enlarge the concrete’s application range. In order to further promote the development and application of fiber-reinforced brick aggregate recycled concrete, the research results regarding its mechanical properties are reviewed in this paper. The effect of the content of broken brick on the mechanical properties of recycled concrete and the effects of different categories and contents of fiber on the basic mechanical properties of recycled concrete are analyzed. The problems to be solved in research on the mechanical properties of fiber-reinforced recycled brick aggregate concrete are presented, and the related research suggestions and prospects are summarized. This review provides a reference for further research in this field and the popularization and application of fiber-reinforced recycled concrete.