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. To both reflect recent experimental and conceptual progress, and distinguish from paper-based capillary microfluidics, we adopt the more recent terminology of capillaric circuits (CCs). We identify three distinct waves of development driven by microfabrication technologies starting with early implementations in industry using machining and lamination, followed by development in the context of micro total analysis systems (μTAS) and lab-on-a-chip devices using cleanroom microfabrication, and finally a third wave that arose with advances in rapid prototyping technologies. We discuss the basic physical laws governing capillary flow, deconstruct CCs into basic circuit elements including capillary pumps, stop valves, trigger valves, retention valves, and so on, and describe their operating principle and limitations. We discuss applications of CCs starting with the most common usage in automating liquid delivery steps for immunoassays, and highlight emerging applications such as DNA analysis. Finally, we highlight recent developments in rapid prototyping of CCs and the benefits offered including speed, low cost, and greater degrees of freedom in CC design. The combination of better analytical models and lower entry barriers (thanks to advances in rapid manufacturing) make CCs both a fertile research area and an increasingly capable technology for user-friendly and high-performance laboratory and diagnostic tests.