How does a magnetic trap work?

Magnetic trapping is a cornerstone of modern ultracold physics and its applications, including quantum information processing, quantum metrology, quantum optics, and high-resolution spectroscopy. Here, a comprehensive analysis and discussion of the basic physics behind the most commonly used magnetic traps used in Bose-Einstein condensation is presented. This analysis includes the quadrupole trap, the time-averaged orbiting potential trap, and the Ioffe-Pritchard trap. The trapping conditions and efficiency of these devices can be determined from simple derivations based on classical electromagnetism, even though they operate on quantum objects.