Spherical multipole (SM) magnetic fields are used for plasma containment. Such magnetic fields are produced by magnetic dipoles symmetrically placed on the sides and the edges of regular polyhedrons. In the paper, field configuration of the high order SM systems is considered and some basic problems regarding the design of SM electromagnets are discussed. Relations are given relating magnetic field, power input, current- and temperature- time characteristics. The construction and operation of the ``Kaktus'' magnet are also described.