The need for NMR selective pulses in magnetic resonance imaging and spectroscopy is reviewed. The shortcomings of the current generation of pulses are discussed and the need for new categories of pulse identified. Strategies for selective pulse design are outlined and two numerical optimization methods, simulated annealing and SPINCALC (a method recently introduced by us: J. T. Ngo and P. G. Morris, Magn. Reson. Med. 5, 217 (1987], are discussed in detail. Their use is illustrated and compared for the design of pi/2 phase-compensated pulses. Both methods require substantial amounts of CPU time, with simulated annealing the more demanding. Unconstrained, simulated annealing also tends to produce pulses with discontinuous waveforms. A crude two-dimensional pulse derived from a low flip angle approximation is illustrated.