The impact of urban air pollution on the environments and human health has drawn increasing concerns from researchers, policymakers and citizens. To reduce the negative health impact, it is of great importance to measure the air pollution at high spatial resolution in a timely manner. Traditionally, air pollution is measured using dedicated instruments at fixed monitoring stations, which are placed sparsely in urban areas. With the development of low-cost micro-scale sensing technology in the last decade, portable sensing devices installed on mobile campaigns have been increasingly used for air pollution monitoring, especially for traffic-related pollution monitoring. In the past, some reviews have been done about air pollution exposure models using monitoring data obtained from fixed stations, but no review about mobile sensing for air pollution has been undertaken. This article is a comprehensive review of the recent development in air pollution monitoring, including both the pollution data acquisition and the pollution assessment methods. Unlike the existing reviews on air pollution assessment, this paper not only introduces the models that researchers applied on the data collected from stationary stations, but also presents the efforts of applying these models on the mobile sensing data and discusses the future research of fusing the stationary and mobile sensing data.