Memristors, or memristive devices, have gained substantial attention as valuable building blocks for neuromorphic computing systems. Their dynamic reconfiguration enables simulation of essential analog synaptic and neuronal functionalities, making them promising candidates for brain-inspired neural network computing. In recent years, conventional thin film materials and low-dimensional nanomaterials have been extensively explored in memristive devices for the development of neuromorphic applications. Despite progress in memristive devices, several technical challenges persist, such as device-to-device uniformity and high device density integration, requiring further improvement at the single device and system level integration. Interface engineering, through careful design of the physical and chemical nature of the interface in the two-terminal memristive device structure, emerges as a promising method to address these challenges. This review highlights the utilization of interface engineering techniques to optimize memristive device behavior, covering both conventional thin film materials and low-dimensional nanomaterials including 0D quantum dots and nanoparticles, 1D nanowire/nanotube, 2D materials, and heterostructures of these nanoscale materials. Two main classes of mechanisms involved in interface engineering, specifically, the electronic and ionic mechanisms for modulating the memristive devices are described in detail. Recent advancements in electronic and optical artificial synaptic and neuronal functionalities and further integration have also been reviewed. This review concludes with the remaining challenges for memristive devices and how interface engineering would be promising for addressing these issues. This comprehensive review serves as a valuable guide for atomic-scale interface engineering in memristive devices and neuromorphic research, while also emphasizing the broader potential of interface engineering in modulating nanoscale dynamic kinetics and enabling various nanoscale devices with exciting physiochemical properties and reconfigurable functionalities.