Implementation of Artificial Intelligence and Machine Learning algorithms on conventional Von Neumann computing architectures are crippled by the memory-wall bottleneck. To overcome these issues, novel computing architectures with high-bandwidth memories, in-memory computing, and near-memory computing capabilities are being developed. Almost all of these architectures will benefit from high-density on-chip non-volatile memories, offered by the emerging non-volatile memory devices. Additionally, emerging memory devices offer rich device physics that can be leveraged for the implementation of novel computing paradigms. This paper will talk about three such emerging memory technologies: Vertical-Thin Film Transistors-Resistive Random Access Memory (V-TFT-RRAMs), Gated-RRAMs, and Ferroelectric Field Effect transistors (FeFETs). A comparative studies of various conventional neuromorphic computing approaches that can be implemented using these devices will be discussed. Finally, materials and device requirements and pending challenges will be discussed by successful realization of the proposed computing approaches. Implementation of Artificial Intelligence and Machine Learning algorithms on conventional Von-Neumann computing architectures are crippled by the memory-wall bottleneck. To overcome these issues, novel computing architectures with high-bandwidth memories, in-memory computing, and near-memory computing capabilities are getting developed. Almost all of these architectures will benefit from high-density on-chip non-volatile memories, offered by the emerging non-volatile memory devices. Additionally, emerging memory devices offer a rich set of device physics that can be leveraged for the implementation of novel computing paradigms. This paper will talk about three such emerging memory technologies: Vertical-Thin Film Transistors-Resistive Random Access Memory (V-TFT-RRAMs), Gated-RRAMs, and Ferroelectric Field Effect Transistors (FeFETs). A comparative studies of various unconventional and brain-inspired neuromorphic computing approaches that can be implemented using these devices will be discussed. Finally, materials and device requirements and pending challenges will be discussed for these device technologies.