Gaseous exhaust of different industries contains dust particles of different chemical precipitates that are harmful for the environment. Electrostatic Precipitators are very often used in industries to filter their gaseous exhaust and to prevent the atmosphere to being polluted. Electrostatic Precipitators are very efficient in their work. Electrostatic Precipitators use the force of the electric field to separate the dust particles from gaseous exhaust. Electrostatic Precipitators charge the dust particles and remove these particles by attracting these charged dust particles toward the collecting plates. The charging of dust particles requires a charging zone. When gas passes through that charging zone, the dust particles in the gas stream become charged and then these charged particles are attracted toward the collecting plates. The design of an Electrostatic Precipitators requires the knowledge of its working principle and the problems that often arise during its working. This thesis is the study of the working and the problems of the Electrostatic Precipitators. The main reason for problems in working of an Electrostatic Precipitator is the dust resistivity. This dust resistivity affects the collection performance of an Electrostatic Precipitator. This thesis also contains the simulation of an Electrostatic Precipitator. In the simulation part, the Electric Potential and the Electric Field of an ESP is modeled in an ideal condition, when no gas is flowing through the ESP. The industrial software Comsol Multiphysics is used for the simulation. A Comsol Multiphysics guide is given in appendix of this thesis report that provides information about using this software.