This thesis examines the modeling of the shock-layer radiative heating associated with hypersonic vehicles entering the atmospheres of Earth and Titan. For Earth entry, flight conditions characteristic of lunar-return are considered, while for Titan entry, the Huygens probe trajectory is considered. For both cases, the stagnation region flowfield is modeled using a two-temperature chemical nonequilibrium viscous shock layer (VSL) approach. This model is shown to provide results that are in agreement with the more computationally expensive Navier-Stokes solutions. A new radiation model is developed that applies the most up-to-date atomic and molecular data for both the spectrum and non-Boltzmann modeling. This model includes a new set of atomic-lines, which are shown to provide a significant increase in the radiation (relative to previous models) resulting from the 1 - 2 eV spectral range. A new set of electronic-impact excitation rates was compiled for the non-Boltzmann modeling of the atomic and molecular electronic states. Based on these new rates, a novel approach of curve-fitting the non-Boltzmann population of the radiating atomic and molecular states was developed. This new approach provides a simple and accurate method for calculating the atomic and molecular non-Boltzmann populations. The newly-developed nonequilibrium VSL flowfield and nonequilibrium radiation models were applied to the Fire II and Apollo 4 cases, and the resulting radiation predictions were compared with the flight data. For the Fire II case, the present radiation-coupled flowfield model provides intensity values at the wall that predicted the flight data better than any other previous study, on average, throughout the trajectory for the both the 0.2 - 6.0 eV and 2.2 - 4.1 eV spectral ranges. The present results over-predicted the calorimeter measurements of total heat flux over most of the trajectory. This was shown to possibly be a result of the super-catalytic assumption for the wall boundary condition, which caused the predicted convective heating to be too high. For the Apollo 4 case, over most of the trajectory the present model over-predicted the flight data for the wall radiative intensity values between 0.2 - 6.2 eV. For the analysis of Huygens entry into Titan, the focus of the radiation model was the CN violet band. An efficient and accurate method of modeling the radiation from this band system was developed based on a simple modification to the smeared rotational band (SRB) model. This modified approach, labeled herein as SRBC, was compared with a detailed line-by-line (LBL) calculation and shown to compare within 5% in all cases. The SRBC method requires many orders-of-magnitude less computational time than the LBL method, which makes it ideal for coupling to the flowfield. The non-Boltzmann modeling of the CN electronic states, which govern the radiation for Huygens entry, is discussed and applied. The radiation prediction resulting from the non-Boltzmann model is up to 70% lower than the Boltzmann result. A new method for treating the escape factor in detail, rather than assuming a value equal to one, was developed. This treatment is shown to increase the radiation from the non-Boltzmann model by about 10%. / Ph. D.