HgTe grown by MBE onto CdTe substrates under excess Hg conditions was found to lead to a columnar void-twin microstructure, with the twins nucleating from the voids. Grown under Hg-deficient conditions, the microstructure of MBE HgTe consisted of columnar polycrystals. Nucleation of the polycrystals occurred only at the commencement of growth. Possible growth and twinning mechanisms are discussed.