In this review we present a general survey regarding the MBE growth of Hg1−xCdxTe and HgTe–CdTe during the last three years. The quality of the films grown by MBE is now comparable with the best material grown by other techniques. We discuss the limitations of the MBE technique, i.e., the low mercury condensation coefficient at 200 °C where the best layers are grown, and the difficulties arising from the growth and the doping control. The poor crystal quality of bulk CdTe substrates is a limitation of any epitaxial layer grown by LPE, OMCVD, or MBE. Thus use of better substrates like (Cd,Zn)Te, Cd(Te,Se), InSb, GaAs, and sapphire could be a solution to this very important problem. We report here for the first time the successful growth by MBE of epitaxial Hg1−xCdxTe layers onto (Cd,Zn)Te, InSb, and GaAs substrates. We discuss the use of superlattices HgTe–CdTe for IR detection devices.