The accurate assessment of creep–fatigue interaction is an important issue for industrial components operating with large cyclic thermal and mechanical loads. An extensive review of different aspects of creep fatigue interaction is proposed in this paper. The introduction of a high temperature creep dwell within the loading cycle has relevant impact on the structural behavior. Different mechanisms can occur, including the cyclically enhanced creep, the creep enhanced plasticity and creep ratchetting due to the creep fatigue interaction. A series of crucial parameters for crack initiation assessment can be identified, such as the start of dwell stress, the creep strain, and the total strain range. A comparison between the ASME NH and R5 is proposed, and the principal differences in calculating the aforementioned parameters are outlined. The linear matching method (LMM) framework is also presented and reviewed, as a direct method capable of calculating these parameters and assessing also the steady state cycle response due to creep and cyclic plasticity interaction. Two numerical examples are presented, the first one is a cruciform weldment subjected to cyclic bending moment and uniform high temperature with different dwell times. The second numerical example considers creep fatigue response on a long fiber reinforced metal matrix composite (MMC), which is subjected to a cycling uniform thermal field and a constant transverse mechanical load. All the results demonstrate that the LMM is capable of providing accurate solutions, and also relaxing the conservatisms of the design codes. Furthermore, as a direct method, it is more efficient than standard inelastic incremental finite element analysis.