Nowadays, epoxy composites are elements of engineering materials and systems. Although they are known as versatile materials, epoxy resins suffer from high flammability. In this sense, flame retardancy analysis has been recognized as an undeniable requirement for developing future generations of epoxy-based systems. A considerable proportion of the literature on epoxy composites has been devoted to the use of phosphorus-based additives. Nevertheless, innovative flame retardants have coincidentally been under investigation to meet market requirements. This review paper attempts to give an overview of the research on flame retardant epoxy composites by classification of literature in terms of phosphorus (P), non-phosphorus (NP), and combinations of P/NP additives. A comprehensive set of data on cone calorimetry measurements applied on P-, NP-, and P/NP-incorporated epoxy systems was collected and treated. The performance of epoxy composites was qualitatively discussed as Poor, Good, and Excellent cases identified and distinguished by the use of the universal Flame Retardancy Index (FRI). Moreover, evaluations were rechecked by considering the UL-94 test data in four groups as V0, V1, V2, and nonrated (NR). The dimensionless FRI allowed for comparison between flame retardancy performances of epoxy composites. The results of this survey can pave the way for future innovations in developing flame-retardant additives for epoxy.