In a hydrodynamic sense, a coral reef is a complex array of obstacles that exerts a net drag force on water moving over the reef. This drag is typically parameterized in ocean circulation models using drag coefficients (CD) or roughness length scales (z0); however, published CD for coral reefs span two orders of magnitude, posing a challenge to predictive modeling. Here we examine the reasons for the large range in reported CD and assess the limitations of using CD and z0 to parameterize drag on reefs. Using a formal framework based on the 3D spatially averaged momentum equations, we show that CD and z0 are functions of canopy geometry and velocity profile shape. Using an idealized two layer model, we illustrate that CD can vary by more than an order of magnitude for the same geometry and flow depending on the reference velocity selected and that differences in definition account for much of the range in reported CD values. Roughness length scales z0 are typically used in 3D circulation models to adjust CD for reference height, but this relies on spatially averaged near bottom velocity profiles being logarithmic. Measurements from a shallow backreef indicate that z0 determined from fits to point measurements of velocity profiles can be very different from z0 required to parameterize spatially averaged drag. More sophisticated parameterizations for drag and shear stresses are required to simulate 3D velocity fields over shallow reefs; in the meantime, we urge caution when using published CD and z0 values for coral reefs.