Excessive release of nitrogen (e.g., ammonia and organic nitrogen) into natural water systems can cause serious environmental problems such as algal blooms and eutrophication in lakes and rivers, threating the aquatic life and ecosystem balance. Membrane aerated biofilm reactor (MABR) and anaerobic ammonia oxidation (Anammox) are new technologies for wastewater treatment with an emphasis on energy-efficient nitrification and denitrification. Microplastic (MP) is an emerging contaminant in wastewater and sludge treatment that has a negative effect on the environment and public health. For these relatively new technologies and contaminants, mathematical models can enhance our understanding of the removal mechanisms, such as reaction kinetics and mass transport. In this study, mathematical models were developed and utilized to simulate the removal of nitrogen and MP in biological reactions in wastewater treatment processes. Firstly, a comprehensive MABR model was developed and calibrated using a pilot-scale MABR operation data to estimate the important process parameters where it was found that biofilm thickness, liquid film thickness and C/N ratio are key parameters on nitrification and denitrification. Secondly, a mathematical model for Anammox process was developed and calibrated using previous experimental results to simulate the wastewater treatment using Anammox process, reflecting the importance of dissolved oxygen on the nitrogen removal using Anammox bacteria. Thirdly, a granule-based Anammox mathematical model was built and calibrated using other simulation results from previous Anammox studies, showing the significance of operational conditions (e.g., granule diameter and dissolved oxygen) on the success of Anammox enrichment process. Fourthly, an enzyme kinetic mathematical model was constructed and calibrated with lab-scale experiments to simulate the MP reduction using hydrolytic enzymes under various experimental conditions where it was found that anaerobic digesters can be an innovative solution for MP removal during the wastewater treatment processes. Based on the main findings in this study, it can be concluded that mathematical models calibrated with various experimental results are efficient tools for determining the important operational parameters on the nitrogen and MP removal and helping in the design and operation of large-scale removal applications. / Thesis / Doctor of Philosophy (PhD) / Nitrogen and microplastic (MP) are serious contaminants in wastewater that can cause critical environmental and public health problems. Nitrogen can cause algal blooms, threatening the aquatic ecosystem while MP can be ingested by the biota (e.g., fish and seabirds), causing serious damage in the food chain. Nitrogen removal in the conventional biological wastewater treatment is relatively expensive, requiring high energy cost and large footprint for the wastewater treatment facilities. MP removal is also difficult in the conventional wastewater and sludge treatment processes. Therefore, new technologies, including membrane aerated biofilm reactor (MABR), anaerobic ammonia oxidation (Anammox) and hydrolytic enzymes processes, are implemented to improve the nitrogen and MP removal with a reduced energy and resources consumption in wastewater and sludge treatment processes. Numerical models are considered as an efficient tool for better understanding of these novel technologies and the competitive biological reaction in these technologies coupled with accurate estimation of process rates of the reactions. In this thesis, different numerical models were developed and calibrated to estimate the important model parameters, assess the effect of operational conditions on the removal mechanisms and determine the dominant parameters on the removal of nitrogen and MP in the wastewater treatment processes. These numerical models can be used for better understanding of the removal mechanisms of nitrogen and MP, helping in the design and operation of removal systems and addressing novel technologies in large-scale nitrogen and MP removal applications.