Fiber-reinforced ceramic matrix composites (FRCMCs) have emerged as critical materials for high-temperature applications in aerospace, gas turbines, and nuclear energy due to their exceptional high-temperature resistance, lightweight properties, high strength, and corrosion resistance. As thermal structure materials, the fracture strength of these composites is a critical mechanical performance indicator, which is significantly influenced by the high-temperature oxidation environment encountered during service. Establishing scientific and effective high-temperature strength prediction models that can reveal physical mechanisms plays a very significant role in material selection, performance assessment, and application. In this part, this paper presents a comprehensive review of factors influencing the strength of FRCMCs in service environments, summarizes mainstream strength models, and proposes future research directions in high-temperature strength theory. Besides, the temperature-dependent fracture strength models for single-phase ceramics without fitting parameters based on the force-heat equivalence energy principle developed by the author have been elaborated in detail. On this basis, the physic-based temperature-dependent fracture strength models for FRCMCs mainly including cross-ply FRCMCs, 2D woven FRCMCs, and SiC fiber-reinforced ceramic matrix composites have been established. These models consider the effects of temperature, the strength of constituent materials, residual thermal stress, as well as fiber oxidation. Meanwhile, the above models have been well validated by the experimental results. The developed models provide theoretical guidance and scientific basis for material selection, performance evaluation, and optimization in extreme service environments.