A modular microfluidic system includes a plurality of discrete microfluidic modules each capable of performing at least one operation and at least one microfluidic coupling device for fluidically coupling the modules to perform a sequence of operations. The microfluidic modules and coupling devices may be constructed according to various techniques. In one embodiment, coupling devices are fabricated from multiple layers and each include a fluidic inlet port, a fluidic outlet port, and at least one sandwiched stencil layer having a microfluidic channel formed therein. Also described are integrated microfluidic systems and methods capable of performing various sequences of operations.