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Techniques, such as micropipette aspiration and optical tweezers, are widely used to measure cell mechanical properties, but are generally labor-intensive and time-consuming, typically involving a difficult process of manipulation. In the past two decades, a large number of microfluidic devices have been developed due to the advantages they offer over other techniques, including transparency for direct optical access, lower cost, reduced space and labor, precise control, and easy manipulation of a small volume of blood samples. This review presents recent advances in the development of microfluidic devices to evaluate the mechanical response of individual red blood cells (RBCs) and microbubbles flowing in constriction microchannels. Visualizations and measurements of the deformation of RBCs flowing through hyperbolic, smooth, and sudden-contraction microchannels were evaluated and compared. In particular, we show the potential of using hyperbolic-shaped microchannels to precisely control and assess small changes in RBC deformability in both physiological and pathological situations. Moreover, deformations of air microbubbles and droplets flowing through a microfluidic constriction were also compared with RBCs deformability.