During the last decade, there is an ever-growing concern regarding the future of CMOS technology, as well as the emerging difficulties on handling upcoming technological issues related with silicon transistors' dimensions, electrical power, energy consumption, and last but not least reaching the physical limits of this technology. At the same time, new computing alternatives beyond the classical computing systems, namely von Neumman architectures, are heavily sought after to tackle energy and memory-wall problems. In this talk, we focus on a hybrid analogue computational circuit-level system with unipolar memristor nanodevices connected in oscillatory networks and based on wave-like propagation of information. These methods are inspired by biochemical processes occurring in nature. The proposed insightful electrochemical wave propagation is apparent in many natural and biological systems and is modelled with powerful, inherently parallel computational tools, like Cellular Automata (CAs). This framework enables us to further proceed into realising alternative types of computations executed on the designed, modelled and fabricated memristor nanodevices, which are finally employed for the design and development of wave based electronic computational units. The proposed nanoelectronic memristive oscillatory networks will be in the advantageous position to perform both classical and unconventional calculations, like multi-digit, in memory and neuromorphic, to name a few of them. Thus, we will have a powerful tool targeting beyond the existing von Neumann information processing techniques and alleviating the aforementioned disadvantages associated with them.