Characterization of the extensional rheometry of fluids with complex microstructures is of great relevance to the optimization of a wide range of industrial applications and for understanding various natural processes, biological functions, and diseases. However, quantitative measurement of the extensional properties of complex fluids has proven elusive to researchers, particularly in the case of low viscosity, weakly elastic fluids. For some time, microfluidic platforms have been recognized as having the potential to fill this gap and various approaches have been proposed. This review begins with a general discussion of extensional viscosity and the requirements of an extensional rheometer, before various types of extensional rheometers (particularly those of microfluidic design) are critically discussed. A specific focus is placed on microfluidic stagnation point extensional flows generated by cross-slot type devices, for which some important developments have been reported during the last 10 years. Additional emphasis is placed on measurements made on relevant biological fluids. Finally, the operating limits of the cross-slot extensional rheometer (chiefly imposed by the onset of elastic and inertial flow instabilities) are discussed.