Soft and conductive nanomaterials like carbon nanotubes, graphene, and nanowire scaffolds have expanded the family of ultraflexible microelectrodes that can bend and flex with the natural movement of the brain, reduce the inflammatory response, and improve the stability of long-term neural recordings. However, current methods to implant these highly flexible electrodes rely on temporary stiffening agents that temporarily increase the electrode size and stiffness thus aggravating neural damage during implantation, which can lead to cell loss and glial activation that persists even after the stiffening agents are removed or dissolve. A method to deliver thin, ultraflexible electrodes deep into neural tissue without increasing the stiffness or size of the electrodes will enable minimally invasive electrical recordings from within the brain. Here we show that specially designed microfluidic devices can apply a tension force to ultraflexible electrodes that prevents buckling without increasing the thickness or stiffness of the electrode during implantation. Additionally, these "fluidic microdrives" allow us to precisely actuate the electrode position with micron-scale accuracy. To demonstrate the efficacy of our fluidic microdrives, we used them to actuate highly flexible carbon nanotube fiber (CNTf) microelectrodes for electrophysiology. We used this approach in three proof-of-concept experiments. First, we recorded compound action potentials in a soft model organism, the small cnidarian Hydra. Second, we targeted electrodes precisely to the thalamic reticular nucleus in brain slices and recorded spontaneous and optogenetically evoked extracellular action potentials. Finally, we inserted electrodes more than 4 mm deep into the brain of rats and detected spontaneous individual unit activity in both cortical and subcortical regions. Compared to syringe injection, fluidic microdrives do not penetrate the brain and prevent changes in intracranial pressure by diverting fluid away from the implantation site during insertion and actuation. Overall, the fluidic microdrive technology provides a robust new method to implant and actuate ultraflexible neural electrodes.