This paper deals with the growth by molecular beam epitaxy of semimetallic (rare-earth group V element) compounds on III-V semiconductors. Results are presented, first on the Er-Ga-As and Er-Ga-Sb ternary phase diagrams, second on the lattice-mismatched ErAs/GaAs (δa ≈ +1.6%), YbAs/GaAs (δa/a = +0.8%), and ErSb/GaSb (δa/a ≈ +0.2%) heterostructures, and third on the lattice-matched Sc0.3Er0.7As/GaAs and Sc0.2Yb0.8As/GaAs systems (δa/a < 0.05%). Finally the growth of YbSb2 on GaSb(001) is reported. The studies made in situ by reflection high-energy electron diffraction (RHEED) and x-ray photoelectron diffraction and ex situ by x-ray diffraction, transmission electron microscopy, He+ Rutherford backscattering, and photoelectron spectroscopy are presented. We discuss the atomic registry of the epitaxial layers with respect to the substrates, the appearance of a mosaic effect in lattice-mismatched structures, and the optical and electrical properties of the semimetallic films. The problems encountered for III-V overgrowth on these compounds (lack of wetting and symmetry-related defects) are commented on, and we underline the interest of compounds as YbSb2 which avoid the appearance of inversion defects in the GaSb overlayers.