Neuromorphic computing and engineering has been the focus of intense research efforts that have been intensified recently by the mutation of Information and Communication Technologies (ICT). In fact, new computing solutions and new hardware platforms are expected to emerge to answer to the new needs and challenges of our societies. In this revolution, lots of candidates technologies are explored and will require leveraging of the pro and cons. In this perspective paper belonging to the special issue on neuromorphic engineering of Journal of Applied Physics, we focus on the current achievements in the field of organic electronics and the potentialities and specificities of this research field. We highlight how unique material features available through organic materials can be used to engineer useful and promising bioinspired devices and circuits. We also discuss about the opportunities that organic electronic are offering for future research directions in the neuromorphic engineering field.