An important technical and economic consideration in designing the prospective direct drive inertial fusion energy (IFE) reactor is the determination of a suitable mechanism for tritium breeding from neutrons produced in the initial reaction. A comprehensive review has been undertaken to determine the optimal breeding material, examining several candidate compounds. These include ceramic breeding pebbles as well as liquid 83Pb-17Li (Pb-Li) and (LiF)2BeF2 (FLiBe). In this study, the compounds are evaluated based on chemical and physical properties, structural requirements, feasibility, hazards, and costs of application. Preliminary results seem to indicate that, of the liquid breeding materials, FLiBe may be the more practical option, due to its mechanical feasibility and the relative projected efficiency of blanket design. Likewise, lithium metatitanate (Li2TiO3) appears to be a viable ceramic material. However, much remains to be investigated, particularly the properties of breeder and structural materials in the specific conditions of a reactor. Further work in this area will require theoretical modeling as well as practical trials, currently planned in other progenitor reactor designs. This paper will present the results of the analysis of these candidate breeder materials.