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This review article describes the performance of the magnetic field measuring and monitoring systems for the Compact Muon Solenoid (CMS) detector. To cross-check the magnetic flux distribution obtained with the CMS magnet model, four systems for measuring the magnetic flux density in the detector volume were used. The magnetic induction inside the 6 m diameter superconducting solenoid was measured and is currently monitored by four nuclear magnetic resonance (NMR) probes installed using special tubes outside the barrel hadron calorimeter. Two more NRM probes were installed at the faces of the tracking system. The field inside the superconducting solenoid was precisely measured in 2006 in a cylindrical volume of 3.448 m in diameter and 7 m in length using 10 three-dimensional (3D) B-sensors based on the Hall effect. These B-sensors were installed on each of the two propeller arms of an automated field-mapping machine. In addition to these measurement systems, a system for monitoring the magnetic field during the CMS detector operation has been developed. Inside the solenoid in the horizontal plane, 4 3D B-sensors were installed at the faces of the tracking detector. Twelve 3D B-sensors were installed on the surfaces of the flux-return yoke nose disks. Seventy 3D B-sensors were installed in the air gaps of the CMS magnet yoke. A specially developed flux loop technique was used for the most complex measurements of the magnetic flux density inside the steel blocks of the CMS magnet yoke. The flux loops are installed in 22 sections of the flux-return yoke blocks. The areas enclosed by these coils varied from 0.3 to 1.59 m$^{2}$ in the blocks of the barrel wheels and from 0.5 to 1.12 m$^{2}$ in the blocks of the yoke endcap disks. The development of these systems and the results of the magnetic flux density measurements across the CMS magnet are presented and discussed in this review article.