The basic problems can be summarized in terms of (a) the internal kinematics, including the factors tending to dissipate the system or degrade its energy; (b) the stability of the system as a whole; (c) the initial formation, which in the view adopted here, is to be done by injection in an external magnetic field, or by some repetitive cycle of injection, acceleration and storage. Item (a) involves Coulomb scattering, especially multiple, and radiation arising from motion in the total field. The losses are described in terms of equivalent injection currents necessary to maintain a fictitious system with arbitrarily prescribed characteristics. Item (b) is discussed, mainly with reference to the ``kink'' instability in terms of a dynamical analogue, the breakdown of which leads to a formulation of the usually accepted necessary condition for stability. A stronger condition is also suggested, which, however, is probably much more than sufficient. The experimental difficulties of item (c) are discussed in only a general way, with no definite conclusions being drawn.