HgCdTe is currently the dominant material for infrared sensing and imaging, and is usually grown on lattice-matched bulk CdZnTe (CZT) substrates. There have been significant recent efforts to identify alternative substrates to CZT as well as alternative detector materials to HgCdTe. In this dissertation research, a wide range of transmission electron microscopy (TEM) imaging and analytical techniques was used in the characterization of epitaxial HgCdTe and related materials and substrates for third generation IR detectors. ZnTe layers grown on Si substrates are considered to be promising candidates for lattice-matched, large-area, and low-cost composite substrates for deposition of II-VI and III-V compound semiconductors with lattice constants near 6.1 Å. After optimizing MBE growth conditions including substrate pretreatment prior to film growth, as well as nucleation and growth temperatures, thick ZnTe/Si films with high crystallinity, low defect density, and excellent surface morphology were achieved. Changes in the Zn/Te flux ratio used during growth were also investigated. Small-probe microanalysis confirmed that a small amount of As was present at the ZnTe/Si interface. A microstructural study of HgCdTe/CdTe/GaAs (211)B and CdTe/GaAs (211)B heterostructures grown using MBE was carried out. High quality MBE-grown CdTe on GaAs(211)B substrates was demonstrated to be a viable composite substrate platform for HgCdTe growth. In addition, analysis of interfacial misfit dislocations and residual strain showed that the CdTe/GaAs interface was fully relaxed. In the case of HgCdTe/CdTe/ GaAs(211)B, thin HgTe buffer layers between HgCdTe and CdTe were also investigated for improving the HgCdTe crystal quality. A set of ZnTe layers epitaxially grown on GaSb(211)B substrates using MBE was studied using high resolution X-ray diffraction (HRXRD) measurements and TEM characterization in order to investigate conditions for defect-free growth. HRXRD results gave critical thickness estimates between 350 nm and 375 nm, in good agreement with theoretical predictions. Moreover, TEM results confirmed that ZnTe layers with thicknesses of 350 nm had highly coherent interfaces and very low dislocation densities, unlike samples with the thicker ZnTe layers.