The rich diversity of man-made complex fluids and naturally occurring biofluids is opening up new opportunities for investigating their flow behavior and characterizing their rheological properties. Steady shear viscosity is undoubtedly the most widely characterized material property of these fluids. Although widely adopted, macroscale rheometers are limited by sample volumes, access to high shear rates, hydrodynamic instabilities, and interfacial artifacts. Currently, microfluidic devices are capable of handling low sample volumes, providing precision control of flow and channel geometry, enabling a high degree of multiplexing and automation, and integrating flow visualization and optical techniques. These intrinsic advantages of microfluidics have made it especially suitable for the steady shear rheology of complex fluids. In this paper, we review the use of microfluidics for conducting shear viscometry of complex fluids and biofluids with a focus on viscosity curves as a function of shear rate. We discuss the physical principles underlying different microfluidic viscometers, their unique features and limits of operation. This compilation of technological options will potentially serve in promoting the benefits of microfluidic viscometry along with evincing further interest and research in this area. We intend that this review will aid researchers handling and studying complex fluids in selecting and adopting microfluidic viscometers based on their needs. We conclude with challenges and future directions in microfluidic rheometry of complex fluids and biofluids.