Since 2010s, China has experienced a large-scale air pollution issue; the underlying mechanisms are yet to be fully understood. To capture the spatial and temporal variation of air pollutants, we explore several computational approaches including observational data analysis (surface and remote-sensing measurements), machine learning methods and analytical mathematical models. For example, the analysis of monitoring station data from 2015 to 2017 shows that the annual average of SO2 declined by 29.07% nationally, revealing the effectiveness of clean-air policy enforcement after the 11th five-year plan. In addition, we utilize TROPOMI (TROPOspheric Monitoring Instrument) NO2 Level 2 data (converted to Level 3 data) to analyze to what extent the lockdown policy improved the air quality in major city clusters of China, including Jing-Jin-Ji, Yangtze River Delta and Pearl River Delta. It turns out that the tropospheric NO2 decreased by more than 30% in year-to-year comparison within these regions. Taking into account factors such as meteorology variation, a machine learning method is incorporated to evaluate the lockdown policy effects, which yields decline trends that are consistent with those from the surface measurements. Comparison of machine learning results with monitoring station observation data further indicates that the NO2 concentrations during lockdown period in 2020 decreased by about 30% on average in the three regions, compared with those in the same period in 2019. Besides, we briefly investigate the mathematical principles in air pollution modeling like the dispersion model.