Thermal drawing processes can be used to make multifunctional, high-resolution neural probes for neural recording and stimulation. An exemplary neural probe may include one or more conductive fibers or microelectrodes coated with two or more layers of insulating material, at least one of which is partially etched to expose a tip at the neural probe's distal end. The conductive fibers conduct electrical signals (e.g., neural spikes or electrical stimulation) between the tip and the neural probe's proximal end. Optional optical and fluidic waveguides may guide light and fluid, respectively, between the tip and the proximal end. A neural probe may be flexible enough for long-term (chronic) implantation in neural tissue (e.g., the brain) without excessive tissue damage, even during movement of the brain in the skull. The probe may be made from biocompatible materials, such as insulating and conductive polymers, that have negligible (insignificant) interaction with the surrounding tissue.