The highly efficient computation of the brain relies on its plastic and reconfigurable nature, enabling complex computations and maintenance of vital functions with a remarkably low power consumption of only ~20 W. First efforts to leverage brain-inspired computational principles have led to the introduction of artificial neural networks (ANNs) that revolutionized information processing and daily life. The relentless pursuit of the definitive computing platform is now pushing researchers towards the investigation of novel solutions to emulate specific brain features (such as synaptic plasticity) to allow local and energy efficient computations. The development of such devices may also be pivotal in addressing major challenges of a continuously aging world, including the treatment of neurodegenerative diseases. To date, the neuroelectronics field has been instrumental in deepening our understanding of how neurons exchange information, owing to the rapid development of silicon-based platforms for neural recordings and stimulation. However, this approach still does not allow for in loco processing of the observed biological signals due to two aspects. Firstly, silicon chips applying conventional processing are simply too power hungry to be embedded into the brain. Secondly, despite the success of silicon-based devices in electronic applications, they are ill-suited for directly interfacing with biological tissue. A cornucopia of solutions has therefore been proposed in the last years to obtain neuromorphic materials to create effective biointerfaces and enable reliable bidirectional communication with neurons. Organic conductive materials are not only highly biocompatible and able to electrochemically transduce biological signals, but also promise to include neuromorphic features, such as neuro-transmitter mediated plasticity and learning capabilities. Furthermore, organic electronics, relying on mixed electronic/ionic conduction mechanism, can be efficiently coupled with biological neural networks, while still communicating with silicon-based electronics. We envision neurohybrid systems that integrate silicon-based and organic electronics-based neuromorphic technologies to create active artificial interfaces with biological tissues.