Fluorine NMR spectroscopy has diverse applications, including characterization of chemical reaction mechanisms, protein structure-function studies, and solid-state NMR characterization of crystalline, amorphous, and soft materials. Computational methods have aided in assigning and interpreting chemical shifts, with wide use in solid-state NMR spectroscopy. Work to understand fluorine chemical shifts has been aided by computational methods. So-called "normal" chemical shift behaviour can be understood to arise from ground-state electron density, in which diamagnetic or Lamb shielding dominates. Meanwhile, electronic structure methods indicate that many instances of "reverse" chemical shift behaviour can be understood to be dominated by paramagnetic shielding effects, which arise from the coupling of occupied and unoccupied molecular orbitals in the presence of a magnetic field. Calculations using natural chemical shielding analysis are used to delineate contributions from diamagnetic and paramagnetic shielding of fluorine nuclei in a set of aromatic molecules and aliphatic compounds, some of which exhibit reverse chemical shift behaviour. An overview of recent advances to assign and interpret chemical shifts in complex environments is presented.