Significant progress has been made in the technology for MBE growth of HgCdTe infrared focal-plane arrays on Si substrates since the initial demonstration of MBE HgCdTe-on- Si heteroepitaxy in 1989. In 1995, the first all-MBE-grown detector arrays on Si were produced through direct MBE growth of (112)B-oriented II-VI films on Si without III-V initiation layers, culminating in detector performance comparable to LPE-grown detectors on bulk CdZnTe substrates. This achievement was enabled by the development of two key contributing technologies: CdTe on Si buffer layer growth and HgCdTe p-on-n double-layer heterojunction growth using p-type chemical doping with As. The MBE process for deposition of high crystalline quality CdTe buffer layers has been developed so that x-ray rocking curve FWHM less than 75 arc-sec and near-surface etch pit densities (EPD) of 2 multiplied by 106 cm-2 are routinely achievable for 9-micrometer-thick CdTe buffer layers. The dependence of CdTe EPD on ZnTe initiation layer thickness, insertion of CdTe/CdZnTe strained layer superlattices, and thermal cycling to cryogenic temperatures has been investigated and is reviewed. HgCdTe baselayers deposited by MBE on these CdTe/Si composite substrates exhibit x-ray FWHM as low as 72 arc-sec and EPD of 3 - 20 multiplied by 106 cm-2. To demonstrate the potential for MBE growth of large-area HgCdTe FPAs on Si, detectors with 78 K cutoff wavelength of 7.8 micrometer have been fabricated in this HgCdTe/Si epitaxial material with array-average R0A product of 1.64 multiplied by 104 (Omega) -cm2 (0 FOV).