The rheological characterization of human blood, through modeling and analysis of steady state, transient, and oscillatory shear flows, has made tremendous progress recently. Due to the aggregation of red blood cells at low shear rates, many recent models for blood rheology include a structural, thixotropic component with one of the most recent attempts unifying this approach with a viscoelastic formulation. We will show how these models, along with proposed modifications to another recent structural, kinetic thixotropy model, can improve modeling predictions. Results are compared to the Maxwell-like Bautista-Manero-Puig model, the Oldroyd-8 inspired viscoelastic Anand-Kwack-Masud model, a viscoelastic-thixotropic model from Blackwell and Ewoldt, and the Herschel-Bulkley model. We explore the weaknesses of the legacy blood models and then demonstrate the efficacy of the newly improved models for modeling human blood steady state and transient shear rheology to predict oscillatory shear flow.