We present a comparison of some of the most used iterative Fourier transform algorithms (IFTA) for the design of continuous and multilevel diffractive optical elements (DOE). Our aim is to provide optical engineers with advice for choosing the most suited algorithm with respect to the task. We tackle mainly the beam-shaping and the beam-splitting problems, where the desired light distributions are almost binary. We compare four recent algorithms, together with the historical error-reduction and input-output methods. We conclude that three of these algorithms are interesting for continuous-phase kinoforms, and two, namely the three-step method proposed by Wyrowski and the over-compensation of Prongué, still perform well with multilevel- and binary-phase DOE. © 2004 Society of Photo-Optical Instrumentation Engineers.