The widespread adoption of microfluidic devices among the neuroscience and neurobiology communities has enabled addressing a broad range of questions at the molecular, cellular, circuit, and system levels. Here, we review biomedical engineering approaches that harness the power of microfluidics for bottom-up generation of neuronal cell types and for the assembly and analysis of neural circuits. Microfluidics-based approaches are instrumental to generate the knowledge necessary for the derivation of diverse neuronal cell types from human pluripotent stem cells, as they enable the isolation and subsequent examination of individual neurons of interest. Moreover, microfluidic devices allow to engineer neural circuits with specific orientations and directionality by providing control over neuronal cell polarity and permitting the isolation of axons in individual microchannels. Similarly, the use of microfluidic chips enables the construction not only of 2D but also of 3D brain, retinal, and peripheral nervous system model circuits. Such brain-on-a-chip and organoid-on-a-chip technologies are promising platforms for studying these organs as they closely recapitulate some aspects of in vivo biological processes. Microfluidic 3D neuronal models, together with 2D in vitro systems, are widely used in many applications ranging from drug development and toxicology studies to neurological disease modeling and personalized medicine. Altogether, microfluidics provide researchers with powerful systems that complement and partially replace animal models.