Asymmetry has emerged as a critical design strategy for implementing essential neuromorphic functionalities, such as directional signal propagation, programmable plasticity, and bio-inspired dynamics. This principle involves deliberately breaking symmetry at various scales, which introduces unique physical phenomena including spontaneous built-in fields, anisotropic carrier transport, and memristive switching, which are foundational to synaptic and neuronal emulation. Despite growing research, a systematic synthesis of how asymmetry function across different design levels is lacking, hindering the development of guiding design principles. This review bridges this gap by systematically examining asymmetric engineering across three levels: materials, structures, and device. Benefiting from the inherent structural and electronic versatility of two-dimensional (2D) materials, their unique physical properties arising from such multi-level asymmetry for emulating and regulating synaptic plasticity are analyzed to demonstrate the resultant functional diversity and tunability of neuromorphic devices. Furthermore, existing challenges are discussed and a forward-looking perspective on integrating multiple asymmetries and extending the concept to circuit and system levels is provided. This work aims to establish a coherent design framework and provide a unique pathway for developing next-generation neuromorphic intelligent hardware based on 2D materials.
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