The late-3d transition-metal diatomic fluorides MF = FeF, CoF, NiF, and CuF have been studied using variational multireference (MRCI) and coupled-cluster [RCCSD(T)] methods, combined with large to very large basis sets. We examined a total of 35 (2S+1)vertical bar Lambda vertical bar states, constructing as well 29 full potential energy curves through the MRCI method. All examined states are ionic, diabatically correlating to M++F-(1(S)). Notwithstanding the "eccentric" character of the 3d transition metals and the difficulties to accurately be described with all-electron ab initio methods, our results are, in general, in very good agreement with available experimental numbers.