This article presents an integrated microfluidic system that is capable of programmably metering, entrapping, coalescing, addressably storing, retrieving and manipulating emulsion droplets. A multilayer, flexible PDMS chip with specially designed fluidic channels dynamically reconfigured by pneumatically actuated diaphragms is utilized to integrate a variety of droplet manipulation schemes. Once droplets are formed, their motions are coordinated by a 2D multiplexing scheme, which exploits the bidirectional movement of diaphragms to implement a random-access microarray. In the prototype demonstration, a PDMS molding and bonding process is used to fabricate the proposed microfluidic system. Emulsion droplets with desired volumes and compositions are produced, addressably stored, manipulated and retrieved from a 4 × 4 array, which employs just 4 (= 2 × log24) control inputs for the operation. It has been demonstrated that (1) the integration of droplet manipulation and 2D multiplexing schemes can be achieved readily using bidirectional diaphragm valves, (2) multiplexing of an N × N array could be realized utilizing only 2 × log2N control inputs and (3) a multifunctional, random-access microarray can be accomplished employing a multilayer PDMS chip. As such, the demonstrated random-access microarray could potentially serve as a platform for continuous tracking and multistep processing of emulsion droplets, which is desired for various biological and chemical applications.