This mini-review provides a brief overview of recent devices that use networks of elastomeric valves to minimize or eliminate the need for interconnections between microfluidic chips and external instruction lines that send flow control signals. Conventional microfluidic control mechanisms convey instruction signals in a parallel manner such that the number of instruction lines must increase as the number of independently operated valves increases. The devices described here circumvent this "tyranny of microfluidic interconnects" by the serial encoding of information to enable instruction of an arbitrary number of independent valves with a set number of control lines, or by the microfluidic circuit-embedded encoding of instructions to eliminate control lines altogether. Because the parallel instruction chips are the most historical and straightforward to design, they are still the most commonly used approach today. As requirements for instruction complexity, chip-to-chip communication, and real-time on-chip feedback flow control arise, the next generation of integrated microfluidic circuits will need to incorporate these latest interconnect flow control approaches.