This paper reports our attempts in developing an integrated multiscale mathematical model to describe the wire-plate-type electrostatic precipitator (ESP), aiming to understand the underlying physics and to develop a computer tool for process design and control. In the model, various phenomena in a wide range of length/time scales related to the electric field, gas-particle flow, dust deposition, cake formation, and their interactions are resolved. We apply different numerical methods for different fields in different local regions, leading to various submodels, including a continuum-based electric field model, Euler-Lagrange gas-particle flow model, and discrete-based cake formation model. These submodels are eventually integrated to form an ESP process model, which can generate results useful for better understanding the phenomena and assessing the ESP performance under different conditions.