The main goal of the field of neuromorphic computing is to build machines that emulate aspects of the brain in its ability to perform complex tasks in parallel and with great energy efficiency. Thanks to new computing architectures, these machines could revolutionize high-performance computing and find applications to perform local, low-energy computing for sensors and robots. The use of organic and soft materials in neuromorphic computing is appealing in many respects, for instance, because it allows better integration with living matter to seamlessly meld sensing with signal processing, and ultimately, stimulation in a closed-feedback loop. Indeed, not only can the mechanical properties of organic materials match those of tissue, but also, the working mechanisms of these devices involving ions, in addition to electrons, are compatible with human physiology. Another advantage of organic materials is the potential to introduce novel fabrication techniques relying on additive manufacturing amenable to one-of-a-kind form factors. This field is still nascent, therefore many concepts are still being proposed, without a clear winner. Furthermore, the field of application of organic neuromorphics, where bioinspiration and biointegration are extremely appealing, calls for a co-design approach from materials to systems.