We propose the use of structured microlens arrays to achieve beam shaping, diffusion, and homogenization. Practical results are presented that elucidate the capabilities of structured microlens arrays to perform complex beam shaping tasks, both intensity control and spatial energy distribution, with high efficiency (mostly limited by surface losses) and without the presence of image artifacts. In addition, the refractive nature of the array naturally yields broadband operation with no zero order. The concept of a structured microlens array incorporates both deterministic and random components so that each microlens is individually designed to perform at least some portion of the beam-shaping task. At the same time, the design process ensures that any statistically significant ensemble of microlenses represents a random process described by select probability density functions. As a result, the structured microlens array incorporates the ability of deterministic diffusers to attain optimal scatter properties and the desirable robustness and homogenizing capabilities of random diffusers. These attributes make structured microlens arrays suitable for a wide variety of applications, from excimer laser beam shaping to display screens. We have designed and fabricated structured microlens arrays using a laser writing system that exposes low-contrast photoresist to a modulated beam on a point-by-point basis to produce a continuous surface-relief profile. The method allows the fabrication of arbitrary surface-relief profiles and depths greater than 100 microns. Experimental results include small-angle (less than 1 degree) and large-angle (up to 180-degree span) diffusion, beam shaping into singly- and multiply-connected domains, flat and controlled intensity profiles.