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Recent advancements in memory technologies, particularly cost reduction in memories and the rise of emerging non-volatile memories (NVMs), have spurred widespread adoption of LUT-based approaches. In this article, we first trace the historical evolution of LUT-based computation, then systematically analyze its modern applications across two domains: (1) software implementations, including LUT-based function evaluation and LUT-based neural networks; and (2) hardware architectures, such as LUT in FPGA and LUT-based processing-in-memory (PIM) systems. 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