Respiratory fluid dynamics is integral to comprehending the transmission of infectious diseases and the effectiveness of interventions such as face masks and social distancing. In this research, we present our recent studies that investigate respiratory particle transport via high-fidelity large eddy simulation coupled with the Lagrangian particle tracking method. Based on our numerical simulation results for human respiratory events with and without face masks, we demonstrate that facial masks could significantly suppress particle spreading. The studied respiratory events include coughing and normal breathing through mouth and nose. Using the Lagrangian particle tracking simulation results, we elucidated the transport pathways of saliva particles during inhalation and exhalation of breathing cycles, contributing to our understanding of respiratory physiology and potential disease transmission routes. Our findings underscore the importance of respiratory fluid dynamics research in informing public health strategies to reduce the spread of respiratory infections. Combining advanced mathematical modeling techniques with experimental data will help future research on airborne disease transmission dynamics and the effectiveness of preventive measures such as face masks.