Inspired by the brain's remarkable ability to process information through interconnected neurons, neuromorphic computing aims to emulate the intricate interconnection and information transfer processes characterizing networks of biological neurons. Memristors are widely recognized as the most promising electronic components for enabling the development of neuromorphic computing systems. Their unique ability to emulate synaptic behavior and process information similarly as biological neurons sets them as a cornerstone technology in this field. This review explores the advantages of memristors based on two-dimensional layered halide perovskite (2D LHP) materials, highlighting their ability to mimic synaptic plasticity under a low energy budget. We also discuss recent advancements in 2D LHP memristors and the potential to combine them to build high-performance artificial neural networks. Furthermore, we provide an overview of challenges and future directions for integrating these materials into next-generation neuromorphic systems.