The paper focuses on the convergence between artificial neural networks and biological neural systems, addressing the challenges of establishing a “morphic relation” between the two. The central problem lies in replicating biological neural networks’ dynamic, adaptive, and self-organising properties within artificial constructs. Neuromorphic engineering (NE), an interdisciplinary field at the intersection of neuroscience and computer science, seeks to design artificial neural networks that emulate the structure, function, and temporal dynamics of biological systems. Although artificial neural networks have succeeded in areas like pattern recognition and natural language processing, they often need more fluid adaptability and robustness of biological systems. The paper explores recent advances in deep learning models, in particular deep neural networks, and their ability to capture structure-sensitive cognitive properties. Challenges remain despite promising findings, such as meta-learning techniques and systematic generalization. Deep neural networks, though efficient, often exhibit opaque and fragile learning mechanisms. The paper advocates further exploring the criteria to establish a genuine morphic relation between artificial neural networks and biological neural systems, focusing on structural, functional, and dynamic correspondences to advance the field of neuromorphic engineering.