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This research report defines LLM inference compilation as an independent field that extends traditional offline compilation into a continuous, multi-layered system spanning graphs, kernels, memory management, and runtime scheduling. Unlike static training compilers, inference systems must handle dynamic variables like autoregressive decoding, variable sequence lengths, and the management of KV-cache as a primary data structure. The sources outline a five-layer framework where the traditional boundary between the compiler and the runtime has blurred, effectively turning online scheduling into a compilation problem. Key industry standards like vLLM, TensorRT-LLM, and Triton are analyzed to show how performance now depends on managing memory-bound workloads and "piecewise" graph execution. Ultimately, the report suggests that for modern AI chips, the software stack—specifically the ability to integrate with the MLIR ecosystem and manage dynamic batching—is as critical to success as the silicon itself.