Pulsed magnets are divided into two categories: below 100 T with pulse duration in the range 1 ms-1 s, and above 100 T with pulse duration of order microsecond due to self-destruction of the coil. For both categories, simple scaling laws for the performance are given. For nondestructive magnets, these depend in the first place on the mechanical strength and electrical conductivity of the materials used in coil design; another important parameter is the size of the bore. Together with the energy and power available from the pulsed power supply, this determines peak field and pulse duration. Different types of power supply are discussed, capacitor banks as well as controlled rectification of ac power. For destructive magnets, there is a simple relation between the peak field and the velocity at which the coil structure is expanded by the magnetic force; this can be estimated from shock wave properties of the conductor. The expansion can be neutralized by imploding the coil in a flux compression experiment. High explosives as well as electromagnetic forces have been used for this purpose to obtain fields up to 2800 T. A simple and efficient method is the exploding single-turn coil; this is best suited for experiments up to 300 T.The design and performance of the different magnets is discussed in detail. A few examples for application of these magnets in experiments are given. Prospects for generating higher fields by different methods are discussed, in particular miniaturization on all levels-coils ('micro-magnets') as well as experiments.