Methods and apparatus for pumping and dispensing are provided in which a peristaltic pump (16, 64) pumps liquid from a package (12), and may be integrated in a dispenser (10). The peristaltic pump (64) is adapted for improved accuracy, cleaning, and maintenance. Also provided are improved tubes (18) for peristaltic pumping that are coupled to self-sealing dispensing valves (92, 104, 110, 120).