Sedimentation is one of the most important processes that determine the performance of the activated sludge process, and secondary settling tanks (SSTs) have been investigated with the mathematical models for design and operation optimization. However, the practical application of SST models still remains a challenge due to several difficulties, such as the lack of efficient (high accuracy and low computation cost) solution techniques and reliable model calibration strategies. To facilitate the practical application of SST models, this dissertation focuses on the one-dimensional (1-D) modeling of SSTs, including the numerical analysis to introduce and select efficient solution techniques, sensitivity and practical identifiability analysis to reliably calibrate the 1-D SST models, and evaluation of the implications of SST modeling on the design and control of waste water treatment plants. To improve the understanding of 1-D modeling of SSTs, this dissertation provides a comprehensive literature review of the batch settling methodology and the flux theory, which played a significant role in the early stage of SST investigation. The literature review also contains an explicit introduction of the established 1-D SST models, including the relevant physical laws, various settling behaviors, the constitutive functions, available solution techniques and calibration strategies. As the only available method for analytical solution development of ideal continuous settling model, the method of characteristics has been successfully implemented to investigate the dynamics of SST for various solids loading conditions. This dissertation also introduced the Yee-Roe-Davis method, which able to capture solution discontinuities based on gradient, thus providing numerical solutions with second-order accuracy. By using the method of characteristics as a reference, the convergence analysis of Methods Simplified-Godunov, Godunov and Yee-Roe-Davis shows that all are reliable, since they are able to provide arbitrarily close approximations to the reference solutions as discretization is refined. For a given discretization level, the Yee-Roe-Davis method is most efficient in reducing error, and provides the most accurate approximations. However, this advantage of high accuracy of the Yee-Roe-Davis method is at the cost of larger computation time and coding complexity. To facilitate model calibration, the important parameters for 1-D SST model calibration were identified under non-ideal flow and settling conditions using global sensitivity analysis (GSA). This dissertation also demonstrated that reliable reduction of 1-D SST models can be achieved based on GSA results; for example under the bulking condition, the hindered-compression-dispersion model can be reduced to the hindered-dispersion model without impacting model accuracy. The model uncertainty analysis efficiently evaluates model reduction reliability. In terms of developing batch settling methodology for reliable model calibration, this dissertation found that the hindered settling parameters are more influential in situations where only batch settling data are available, while the sensitivity to compression parameters can be greatly increased if concentration profile observations are included. The practical identifiability analysis further showed that parameter estimates obtained from data sets that only include batch settling data or the concentration profiles cannot generally predict concentration profiles and batch settling curve observations, respectively. Because of the application of local sensitivity functions, the parameter identifiability analysis can be sensitive to the initial parameter value selection. Estimates obtained by identifiable parameter subsets estimation are conditional on the values of fixed parameters. From the view of optimizing the process design and control, this dissertation demonstrated that the bioreactor and SST should be designed as a whole, and a safety constraint can be introduced in the design process to greatly improve the system's efficiency and reliability. A comprehensive selection of the designed alternatives should consider three aspects: economic plausibility, contaminant removal efficiency, and system robustness. Least-cost points can usually be attained, but their locations will vary depending on the weighting of the relative cost factor.