The present invention relates to microfluidic systems, including valves and pumps for microfluidic systems. The valves of the invention include check valves such as diaphragm valves and flap valves. Other valves of the invention include one-use valves. The pumps of the present invention include a reservoir and at least two check valves. The reservoir may be of variable volume. The present invention also relates to a flexible microfluidic system. The present invention additionally relates to a method of making microfluidic systems including those of the present invention. The method includes forming a microfluidic system on a master, connecting a support to the microfluidic system and removing the microfluidic system from the master. The support may remain connected to the microfluidic system or the microfluidic system may be transferred to another substrate. The present invention further relates to a method of manipulating a flow of a fluid in a microfluidic system. This method includes initiating fluid flow in a first direction and inhibiting fluid flow in a second direction and may be practiced with the valves of the present invention.