Fungal laccases (EC 184.108.40.206) are multi-copper oxidases that oxidize a wide variety of substrates. Despite extensive studies, the molecular basis for their diverse activity is unclear. Notably, there is no current way to rationally predict the activity of a laccase toward a given substrate. Such knowledge would greatly facilitate the rational design of new laccases for technological purposes. We report a study of three datasets of experimental Km values and activities for Trametes versicolor and Cerrena unicolor laccase, using a range of protein modeling techniques. We identify diverse binding modes of the various substrates and confirm an important role of Asp-206 and His-458 (T. versicolor laccase numbering) in guiding substrate recognition. Importantly, we demonstrate that experimental Km values correlate with binding affinities computed by MMGBSA. This confirms the common assumption that the protein-substrate affinity is a major contributor to observed Km. From quantitative structure-activity relations (QSAR) we identify physicochemical properties that correlate with observed Km and activities. In particular, the ionization potential, shape, and binding affinity of the substrate largely determine the enzyme's Km for the particular substrate. Our results suggest that Km is not just a binding constant but also contains features of the enzymatic activity. In addition, we identify QSAR models with only a few descriptors showing that phenolic substrates employ optimal hydrophobic packing to reach the T1 site, but then require additional electronic properties to engage in the subsequent electron transfer. Our results advance our ability to model laccase activity and lend promise to future rational optimization of laccases toward phenolic substrates.