In our brains, different neurons make appropriate connections; however, there remain few in vitro models of such circuits. We use an open microfluidic approach to build and study neuronal circuits in vitro in ways that fit easily into existing bio-medical workflows. Dumbbell-shaped circuits are built in minutes in standard Petri dishes; the aqueous phase is confined by fluid walls - interfaces between cell-growth medium and an immiscible fluorocarbon, FC40. Conditions are established that ensure post-mitotic neurons derived from human induced pluripotent stem cells (iPSCs) plated in one chamber of a dumbbell remain where deposited. After seeding cortical neurons on one side, axons grow through the connecting conduit to ramify amongst striatal neurons on the other - an arrangement mimicking unidirectional cortico-striatal connectivity. We also develop a moderate-throughput non-contact axotomy assay. Cortical axons in conduits are severed by a media jet; then, brain-derived neurotrophic factor and striatal neurons in distal chambers promote axon regeneration. As additional conduits and chambers are easily added, this opens up the possibility of mimicking complex neuronal networks, and screening drugs for their effects on connectivity.