Neuromorphic electronics are inspired by the human brain's compact, energy-efficient nature and its parallel-processing capabilities. Beyond the brain, the entire human nervous system, with its hierarchical structure, efficiently preprocesses complex sensory information to support high-level neural functions such as perception and memory. Emulating these biological processes, artificial nerve electronics have been developed to replicate the energy-efficient preprocessing observed in human nerves. These systems integrate sensors, artificial neurons, artificial synapses, and actuators to mimic sensory and motor functions, surpassing conventional circuits in sensor-integrated electronics. Organic synaptic transistors (OSTs) are key components in constructing artificial nerves, offering tunable synaptic plasticity for complex sensory processing and the mechanical flexibility required for applications in soft robotics and bioelectronics. Compared to traditional sensor-integrated electronics, early implementations of organic artificial nerves (OANs) incorporating OSTs have demonstrated a higher signal-to-noise ratio, lower power consumption, and simpler circuit designs along with on-device processing capabilities and precise control of actuators and biological limbs, driving progress in neuromorphic robotics and bioelectronics. This paper reviews the materials, device engineering, and system integration of the OAN design, highlights recent advancements in neuromorphic robotics and bioelectronics utilizing the OANs, and discusses current challenges and future research directions.