Explicitly correlated coupled cluster theory at the CCSD(T*)-F12b level in conjunction with the aug-cc-pV5Z basis set has been used in the calculation of three-dimensional potential energy and dipole moment surfaces for the bifluoride ion (FHF-). An empirically corrected analytical potential energy function (PEF) was obtained by fit to four pieces of accurate spectroscopic information. That PEF was used in variational calculations of energies and wave functions for a variety of rovibrational states of the isotopologues FHF-, FDF-, and FTF-. Excellent agreement with available data from IR laser diode spectroscopy is observed and many predictions, are being made. Unusual isotope effects among the spectroscopic constants and unusual features of the calculated line spectra are discussed.