The BF and BF(+) molecular systems have been thoroughly studied by multireference variational and single reference coupled-cluster methods employing basis sets of sextuple cardinality. Potential energy curves have been constructed for 33 (BF) and 8 (BF(+)) states and the usual molecular parameters have been extracted most of which are in excellent agreement with the available experimental data. A characteristic feature of the BF system is the intense valence-Rydberg interaction in most of the studied states. Its X-state is of (1)Σ(+) symmetry featuring a triple bond of roughly 182 kcal∕mol at re = 1.2631 Å. It is interesting indeed that for the last 50 years it was believed that the charge polarity of BF is B(-)F(+). This is the first time that according to the present high level calculations, it is shown that the polarity of BF is the "normal" one B(+)F(-), with a total charge transfer from B to F of about 0.2 electrons. Removing a rather inactive σ electron we get the X(2)Σ(+) BF(+) state sharing similar bonding features as the X(1)Σ(+) one of the parental molecule.