Leukapheresis is a common extracorporeal procedure for leukodepletion and cellular collection. During the procedure, a patient's blood is passed through an apheresis machine to separate white blood cells (WBCs) from red blood cells (RBCs) and platelets (PLTs), which are then returned to the patient. Although it is well-tolerated by adults and older children, leukapheresis poses a significant risk to neonates and low-weight infants because the extracorporeal volume (ECV) of a typical leukapheresis circuit represents a particularly large fraction of their total blood volume. The reliance of existing apheresis technology on centrifugation for separating blood cells limits the degree to which the circuit ECV could be miniaturized. The rapidly advancing field of microfluidic cell separation holds excellent promise for devices with competitive separation performance and void volumes that are orders of magnitude smaller than their centrifugation-based counterparts. This review discusses recent advancements in the field, focusing on passive separation methods that could potentially be adapted to perform leukapheresis. We first outline the performance requirements that any separation method must meet to replace centrifugation-based methods successfully. We then provide an overview of the passive separation methods that can remove WBCs from whole blood, focusing on the technological advancements made in the last decade. We describe and compare standard performance metrics, including blood dilution requirements, WBC separation efficiency, RBC and PLT loss, and processing throughput, and discuss the potential of each separation method for future use as a high-throughput microfluidic leukapheresis platform. Finally, we outline the primary common challenges that must still be overcome for these novel microfluidic technologies to enable centrifugation-free, low-ECV leukapheresis in the pediatric setting.