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Under different transport mechanisms, blood flow dynamics, heavily linked to the flow shear rate conditions, in “lab-on-a-chip” (LOC) systems are found to result in varying transport phenomena. This Review examines the blood flow patterns in LOC systems through the role of viscoelastic properties such as dynamic blood viscosity and elastic behavior of the red blood cells. The study of blood transport phenomena in LOC systems through key parameters of capillary and electro-osmotic forces is provided through experimental, theoretical, and numerous numerical approaches. The disturbance triggered by electro-osmotic viscoelastic flow is particularly discussed and applied in the enhancement of the mixing and separating capabilities of LOC devices handling blood and other viscoelastic fluids for future research opportunities. Furthermore, the Review identifies the challenges in the numerical modeling of blood flow dynamics under the LOC systems, such as the call for more accurate and simplified blood flow models and the emphasis on numerical studies of viscoelastic fluid flow under the electrokinetic effect. More practical assumptions for zeta potential conditions while studying the electrokinetic phenomena are also highlighted. This Review aims to provide a comprehensive and interdisciplinary perspective on blood flow dynamics in microfluidic systems driven by capillary and electro-osmotic forces.