Paper microfluidics is a rapidly growing subfield of microfluidics in which paper-like porous materials are used to create analytical devices. There is a need for higher performance field-use tests for many application domains including human disease diagnosis, environmental monitoring, and veterinary medicine. A key factor in creating high performance paper-based devices is the ability to manipulate fluid flow within the devices. This critical review is focused on the progress that has been made in (i) the development of fluid flow control tools and (ii) the integration of those tools into paper microfluidic devices. Further, we strive to be comprehensive in our presentation and provide historical context through discussion and performance comparisons, when possible, of both relevant earlier work and recent work. Finally, we discuss the major areas of focus for fluid flow methods development to advance the potential of paper microfluidics for high-performance field applications.