Gradient waveform design is necessary for all MRI pulse sequences. While closed form (analytic) solutions exist for many useful problems and are wide implemented, there are a number of interesting problems for which numerical optimization methods are needed. This talk briefly distinguishes between the analytic and computational approaches to gradient waveform design, then describes a number of applications for which computational approaches provide added value. Four-dimensional phase-contrast (4D-flow) MRI is one example for which time-optimal gradient waveform design can improve overall sequence efficiency by ~20% or more. Diffusion weighted MRI can be optimized for SNR-efficiency and to mitigate eddy currents.