HgCdTe has dominated the high-performance IR detector market for decades. Owing to its numerous merits, including precise energy band structure control and device structure growth, the MBE(molecular beam epitaxy) growth of HgCdTe has become the main tool for fabricating third-generation IR focal plane arrays. CdZnTe is widely considered to be an ideal substrate for HgCdTe epitaxy because of the matched lattice through Zn fraction adjustment. Therefore, HgCdTe/CdZnTe has a high crystal quality with a typical etch pit density in the range of 1.104–1.105 cm-2. However, several limitations, such as high cost, small wafer size, and low yield, still exist in the (211) CdZnTe substrate, which results in high cost and limits the array format size in infrared detectors based on HgCdTe/CdZnTe. Compared with CdZnTe substrates, alternative substrates (e.g., Si, Ge, GaAs, and GaSb) have large wafer size, low cost, and convenience in standard semiconductor equipment, which have the potential to fabricate low-cost high-performance focal plane arrays. The main issue in HgCdTe on alternative substrates is the large lattice mismatch between the substrate and epi-layer (19.3%, 14.3%, 14.4%, and 6.1% for Si, Ge, GaAs, and GaSb, respectively), which is responsible for the high dislocation density of 106–107 cm-2 in HgCdTe films. The high dislocation density hampers the application of this material to long-wavelength and very long-wavelength infrared detectors. The variation in dislocation density with film thickness in the as-grown HgCdTe film grown on an alternative substrate was modeled, and the results from the ρ~1/h law agreed well with the experimental data. This indicates that the dislocation annihilation radius is the leading cause of impeding the dislocation density below 5.106 cm-2 in HgCdTe; thus, dislocation reduction is urgently needed. Moreover, the theory and research progress on three dislocation reduction methods, namely thermal cycle annealing (TCA), dislocation blocking, and mesa dislocation gettering (MDG), are summarized in this paper. Prospects and priorities for future development are also discussed. Overall, TCA and dislocation blocking techniques are likely to be harder in technical breakthroughs and have less development potential in dislocation reduction to below 5. 105 cm-2. By contrast, the MDG technique has shown tremendous development potential and high value in low-cost long-wavelength infrared detectors; however, process integration between the MDG technique and standard focal plane array fabrication is needed.