In this thesis we describe the use of the Faraday effect for operation of an optical magnetometer with hot cesium vapor, a magnetometer with cold cesium atoms and for non-destructive imaging of cold atoms. In the beginning we present a theoretical background of the important phenomena, such as paramagnetic Faraday rotation, Larmor precession and optical pumping. Next, we describe the basic principles of operation of an optically pumped magnetometer, combining a quantum picture with the classical for better understanding. Three schemes of operation are presented, along with an explanation of the underlying principles that enable probing of the magnetometer response and some processes that suppress the perfect operation. Then we describe the realization of the optical magnetometer in the Cold Atom Laboratory, the chosen operation regime and the experimental setup. Some experiments for characterization of optical pumping, magnetometer sensitivity and Faraday rotation are shown, along with radio-frequency background noise measurements. In the next chapter we focus on experimental realization of the cold atom magnetometer that allows us to measure magnetic fields in an atomic cloud with temperatures close to absolute zero. Manipulation of the atomic states with radio-frequency pulses is explained and its effects are measured. In the last chapter we describe the basic principles of a non-destructive Faraday imaging of the cold atoms, the imaging protocol and analysis. We observe the propagation of the cold atom clouds with series of Faraday images and compare destructiveness for different detunings of the imaging beam. In the end, the plans and ideas for future work and development of the experiments in all three areas are described.