Breathing conditions pertaining to nasal obstruction, obstructive sleep apnea, and airflow resistance in the human lower airways have been investigated extensively by researchers over the years. Due to the availability of advanced computer numerical models, such as computational fluid dynamics (CFD), researchers have made progressive studies of airflow characteristic, especially the effects of airflow pressure, velocity and wall shear stress in human obstructive airways. Studies utilizing CFD have enhanced clinical understanding of the physiology and pathophysiology of the respiratory system through the concept of three-dimensional models that facilitate airflow simulation. The main objective of this article is to review recent CFD literature on nasal airflow and lower airway obstruction. The review covers the role of segmentation threshold in the outcome of airflow simulation in the nasal cavity, and results of fluid structure interaction (FSI) and computational fluid dynamics in nasal obstruction and airway collapse in obstructive sleep apnea were also correlated. For models of the lower airways, we evaluated the effect of extra-thoracic airway (ETA) on downstream airflow during simulation against the popular Weibel's model. In the concluding section, we discussed the advantages, limitations, and prospects (precisely with deep machine learning) of computational fluid dynamics in the clinical assessment and investigation of respiratory diseases.