In the era of artificial intelligence and smart automated systems, the quest for efficient data processing has driven exploration into neuromorphic systems, aiming to replicate brain functionality and complex cognitive actions. This review assesses, based on recent literature, the challenges and progress in developing basic neuromorphic systems, focusing on “material-neuron” concepts, that integrate structural similarities, analog memory, retention, and Hebbian learning of the brain, contrasting with conventional von Neumann architecture and spiking circuits. We categorize these devices into filamentary and non-filamentary types, highlighting their ability to mimic synaptic plasticity through external stimuli manipulation. Additionally, we emphasize the importance of heterogeneous neural content to support conductance linearity, plasticity, and volatility, enabling effective processing and storage of various types of information. Our comprehensive approach categorizes fundamentally different devices under a generalized pattern dictated by the driving parameters, namely, the pulse number, amplitude, duration, interval, as well as the current compliance employed to contain the conducting pathways. We also discuss the importance of hybridization protocols in fabricating neuromorphic systems making use of existing complementary metal oxide semiconductor technologies being practiced in the silicon foundries, which perhaps ensures a smooth translation and user interfacing of these new generation devices. The review concludes by outlining insights into developing cognitive systems, current challenges, and future directions in realizing deployable neuromorphic systems in the field of artificial intelligence.