The compounds RECuGa3 (RE = La-Nd, Sm-Gd) were synthesized by various techniques. Preliminary X-ray diffraction (XRD) analyses at room temperature suggested that the compounds crystallize in the tetragonal system with either the centrosymmetric space group I4/mmm (BaAl4 type) or the non- centrosymmetric space group I4mm (BaNiSn3 type). Detailed single-crystal XRD, neutron diffraction, and synchrotron XRD studies of selected compounds confirmed the non-centrosymmetric BaNiSn3 structure type at room temperature with space group I4mm. Temperature-dependent single-crystal XRD, powder XRD, and synchrotron beamline measurements showed a structural transition between centro- and non-centrosymmetry followed by a phase transition to the Rb5Hg19 type (space group I4/m) above 400 K and another transition to the Cu3Au structure type (space group Pm (3) over barm) above 700 K. Combined single-crystal and synchrotron powder XRD studies of PrCuGa3 at high temperatures revealed structural transitions at higher temperatures, highlighting the closeness of the BaNiSn3 structure to other structure types not known to the RECuGa3 family. The crystal structure of RECuGa3 is composed of eight capped hexagonal prism cages [RE4Cu4Ga12] occupying one rare-earth atom in each ring, which are shared through the edge of Cu and Ga atoms along the ab plane, resulting in a three-dimensional network. Resistivity and magnetization measurements demonstrated that all of these compounds undergo magnetic ordering at temperatures between 1.8 and 80 K, apart from the Pr and La compounds: the former remains paramagnetic down to 0.3 K, while superconductivity was observed in the La compound at T = 1 K. It is not clear whether this is intrinsic or due to filamentary Ga present in the sample. The divalent nature of Eu in EuCuGa3 was confirmed by magnetization measurements and X- ray absorption near edge spectroscopy and is further supported by the crystal structure analysis.