Predicting drug concentrations in the blood and at the site of action is the hottest topic in pharmacokinetics (PK). In vitro-in vivo extrapolation (IVIVE) and physiological based pharmacokinetics (PBPK) models are two major PK prediction strategies. However, both IVIVE and PBPK models are considered as immature methodologies due to their poor predictability. The goal of the research is to investigate the discrepancies within IVIVE and PBPK predictions according to first-principles: convection, diffusion, metabolism, and carrier-mediated transport. In Chapter 2, non-permeability limited hepatic elimination under perfusion steady state is examined. The well-stirred model is re-derived from the convection-dispersion-elimination equation when both dispersion and concentration gradient are ignored and re-named as the zero-gradient model. Pang and Rowland’s lidocaine data are re-analyzed. Their data analysis was based on an unfair comparison of the zero-gradient and parallel- tube models at two different efficiency number ranges. The interference of sensitivity greatly biased the comparison. I also show that both theoretical discussions and experimental results indicate that apparent intrinsic clearance and intrinsic clearance could be affected by blood flow and protein binding. In Chapter 3, I discuss permeability limited hepatic elimination under perfusion steady state. Permeability limited elimination is classified to diffusion dominated, carrier-mediated transport mediated, and mixed effects based on drug passage mechanisms. Each of these three drug passage classes is sub-divided to sink condition and finite volume condition based on the boundary conditions of drug passage. In Chapter 4, the discrepancies within IVIVE for both non-permeability limited and permeability limited drugs are explored. The deficiencies in assay design and data analysis of common in vitro metabolism assays are investigated. The scaling/converting equations for both non-permeability limited and permeability limited drugs are derived. In Chapter 5, I focus on transient PK models. Numerical analysis using finite difference and finite volume methods are introduced into the derivation and discussion of transient PBPK models. In addition, the use of partition coefficient in the non-eliminating tissue/organ models is discussed.