Microfluidic devices have not yet evolved into commercial off-the-shelf products. Although highly integrated microfluidic structures, also known as lab-on-a-chip (LOC) and micrototal-analysis-system (TAS) devices, have consistently been predicted to revolutionize biomedical assays and chemical synthesis, they have not entered the market as expected. Studies have identified a lack of standardization and integration as the main obstacles to commercial breakthrough. Soft microfluidics, the utilization of a broad spectrum of soft materials (i.e., polymers) for realization of microfluidic components, will make a significant contribution to the proclaimed growth of the LOC market. Recent advances in polymer science developing novel stimulus-active soft-matter materials may further increase the popularity and spreading of soft microfluidics. Stimulus-active polymers and composite materials change shape or exert mechanical force on surrounding fluids in response to electric, magnetic, light, thermal, or water/solvent stimuli. Specifically devised actuators based on these materials may have the potential to facilitate integration significantly and hence increase the operational advantage for the end-user while retaining cost-effectiveness and ease of fabrication. This review gives an overview of available actuation concepts that are based on functional polymers and points out promising concepts and trends that may have the potential to promote the commercial success of microfluidics.