Bismuth trihalides, BiX 3 (X F, Cl, Br and I) have been thrust into prominence recently due to their close chemical relationship to the halide perovskites of lead, which exhibit remarkable performance as active layers in photovoltaic cells and other optoelectronic devices. In the present work we have used calculations based on density functional theory to explore the energetics and electronic properties of BiX 3 in a variety of known and hypothetical structure types. The results for BiX 3 are compared with those obtained for the halides of the later rare-earths, represented by YX 3 and LuX 3 . The relative thermodynamic stabilities of the known and hypothetical structures are calculated, along with their band gaps. For the BiX 3 systems we have explored the role of 1 lone pair effects associated with Bi(III), and for BiI 3 we have compared the predicted structural behaviour as a function of pressure with the available experimental data. We have also attempted to synthesize LuF 3 in the perovskite-related ReO 3 -type structure, which is predicted to be only ∼ 7.7 kJ mol −1 above the convex hull. This attempt was unsuccessful, but lead to the discovery of a new hydrated phase, (H 3 O)Lu 3 F 10 H 2 O, which is isomorphous with the known ytterbium analogue.