This review considers models with extended Higgs sectors in which there are tree-level flavor-changing neutral currents (FCNC) mediated by scalars. After briefly reviewing models without tree-level FCNC, several models with such currents are discussed. A popular mass-matrix ansatz, in which the flavor-changing couplings are the geometric mean of the individual flavor couplings, is presented. While it provided a target for experimentalists for three decades, it is now being severely challenged by experiments. Couplings expected to be of O(1)

 must be substantially smaller and the ansatz is now not favored. The minimal flavor violation hypothesis is introduced. Then specific models are presented, including the Branco–Grimus–Lavoura models. These models are not yet excluded experimentally, but they are highly predictive and will be tested once heavy Higgs bosons are discovered. We then turn to flavorful models and flavor-changing decays of heavy Higgs bosons, and it is shown that in many of these models, the heavy Higgs could predominantly decay in a flavor-changing manner (such as ct

 or μτ) and experimentalists are encouraged to include these possibilities in their searches.