The Atacama Large Millimeter Array will provide an excellent instrument for direct and indirect detection of extrasolar giant planets and imaging of extrasolar planetary systems at all evolutionary stages. It will excel at subarcsecond imaging of protostellar, protoplanetary and debris disks; gaps and warps in these images will trace the evolution of material within them, including planets. Direct detection of very young, hot protoJupiters can be achieved out to the nearest star-forming regions. Although massive giant planets such as Jupiter itself can be detected only to a few parsecs, objects such as Gl229B might be detected to about 5-10pc. Indirect detection through reflex motions of stars will also be possible.