We present a pick-and-place approach driven by capillarity for highly precise and cost-effective assembly of mesoscopic components onto structured substrates. Based on competing liquid bridges, the technology seamlessly combines programmable capillary grasping, handling, and passive releasing with capillary self-alignment of components onto prepatterned assembly sites. The performance of the capillary gripper is illustrated by comparing the measured lifting capillary forces with those predicted by a hydrostatic model of the liquid meniscus. Two component release strategies, based on either axial or shear capillary forces, are discussed and experimentally validated. The release-and-assembly process developed for a continuously moving assembly substrate provides a roll-to-roll-compatible technology for high-resolution and high-throughput component assembly.