Microfluidics offer economy of reagents, rapid liquid delivery, and potential for automation of many reactions, but often require peripheral equipment for flow control. Capillary microfluidics can deliver liquids in a pre-programmed manner without peripheral equipment by exploiting surface tension effects encoded by the geometry and surface chemistry of a microchannel. Here, we review the history and progress of microchannel-based capillary microfluidics spanning over three decades.