In this chapter, basic principles, methods of generating magnetic fields, magnetic field applications, and numerical methods for the design of magnet structures are briefly introduced and reviewed. Magnets can be classified as permanent magnets and electromagnets. The electromagnets can be operated under steady-state conditions or in a transient (pulsed) mode, and electromagnets can also be classified as nondestructive and destructive magnets. A magnet that uses a permanent magnetic material to generate the magnetic field is called a permanent magnet. The permanent magnets can be classified as high temperature superconductor (HTS) permanent magnets, such as those made from YBa2Cu3O7 (YBCO), and conventional permanent magnets (such as the NdFeB magnets). Scientific instruments and electrical equipment have some specific functions. To realize the functions and reduce the costs, the magnet designer has to achieve an appropriate field strength and distribution by means of a suitable current distribution with a minimum of material. Controlled Vocabulary Terms electromagnets; magnetic fields; permanent magnets