Network structures arise in many applications like for biological tissues, neuron systems, and nanoelectronic devices. Neuronal network structures are inspiring novel neuromorphic computer architectures, overcoming physical scaling limits in traditional hardware. The project NEUROMORPH focuses on the interplay of emerg-ing structures in biological neuron systems and electronic circuit models. The problems we address are formu-lated in terms of nonlinear partial differential systems, including stochastic and nonlocal terms. Examples include transport through ion channels, chemotaxis-fluid systems, mean-field network models, and memristor networks.