We calculate the bulk photovoltaic response of the ferroelectrics BaTiO3 and PbTiO3 from first principles by applying the “shift current” theory to the electronic structure from density functional theory. The first principles results for BaTiO3 reproduce experimental photocurrent direction and magnitude as a function of light frequency, as well as the dependence of current on light polarization, demonstrating that shift current is the dominant mechanism of the bulk photovoltaic effect in BaTiO3. Additionally, we analyze the relationship between response and material properties in detail. Photocurrent does not depend simply or strongly on the magnitude of material polarization, as has been previously assumed; instead, electronic states with delocalized, covalent bonding that is highly asymmetric along the current direction are required for strong shift current enhancements. The complexity of the response dependence on both external and material parameters suggests applications not only in solar energy conversion, but in photocatalysis and sensor and switch type devices as well.