Microfluidic devices are useful in tissue engineering due to the ability to manipulate and direct small volumes of cell-laden solutions with precise control and repeatability. Smart materials offer a responsive, dynamic scaffold by which tissue units, vascular systems, and organoids can be assembled within a microfluidic device. The quick and predictable response of a smart material allows for rapid manufacture of small tissue structures while maintaining a physiologically relevant temperature. Furthermore, smart materials facilitate rapid polymerization, allowing highly controllable geometries to be formed within a micro-channel. Tissue constructs can be formed as fibers, vessels, spheroids, and microparticles through the use of a microfluidic device. Additionally, smart materials can be utilized as pumps, valves, and chambers for fluid manipulation in a channel. Herein, the devices, materials, and approaches used in smart microfluidic systems will be discussed and compared as they relate to tissue engineering. Smart microfluidic systems responsive to chemical stimuli, light sources, and temperature changes are considered and further organized by the final construct of the tissue or cellular network after processing within the device.