Chronically implanted recording electrode arrays linked to prosthetics have the potential to make positive impacts on patients suffering from full or partial paralysis. Such arrays are implanted into the patient's cortical tissue and record extracellular potentials from nearby neurons, allowing the information encoded by the neuronal discharges to control external devices. While such systems perform well during acute recordings, they often fail to function reliably in clinically relevant chronic settings. Available evidence suggests that a major failure mode of electrode arrays is the brain tissue reaction against these implants, making the biocompatibility of implanted electrodes a primary concern in device design. This review presents the biological components and time course of the acute and chronic tissue reaction in brain tissue, analyses the brain tissue response of current electrode systems, and comments on the various material science and bioactive strategies undertaken by electrode designers to enhance electrode performance.