SEMGRASP is a novel method for semantic grasp generation that integrates semantic information into grasp representation. The method introduces a discrete representation that aligns grasp space with semantic space, enabling grasp generation according to language instructions. A Multimodal Large Language Model (MLLM) is fine-tuned to integrate object, grasp, and language within a unified semantic space. A large-scale dataset, CAPGRASP, is compiled with 260k detailed captions and 50k diverse grasps. Experimental results show that SEMGRASP efficiently generates natural human grasps aligned with linguistic intentions. The method is evaluated using metrics such as physical plausibility and semantic consistency. It outperforms existing methods in these metrics. The method is applied in AR/VR and embodied robotics, demonstrating the ability to synthesize dynamic grasp motions. The method's discrete representation is both interpretable and controllable, making it suitable for semantic space alignment. The method is also effective in generating grasps based on language instructions, as demonstrated by experiments. The method's contributions include the introduction of SEMGRASP, a novel grasp discrete representation, and the CAPGRASP dataset. The dataset includes low-level, high-level, and conversational annotations, making it the first of its kind. The method is trained using a VQ-VAE and an MLLM, with the VQ-VAE used for grasp discretization and the MLLM for grasp generation. The method is evaluated on multiple metrics and shows superior performance compared to existing methods. The method is also effective in applications such as AR/VR and embodied robotics, demonstrating the potential for generating more human-like, semantically coherent grasps in various contexts. Limitations include the need for further exploration in two-hand manipulation and end-to-end semantic grasp motion synthesis.SEMGRASP is a novel method for semantic grasp generation that integrates semantic information into grasp representation. The method introduces a discrete representation that aligns grasp space with semantic space, enabling grasp generation according to language instructions. A Multimodal Large Language Model (MLLM) is fine-tuned to integrate object, grasp, and language within a unified semantic space. A large-scale dataset, CAPGRASP, is compiled with 260k detailed captions and 50k diverse grasps. Experimental results show that SEMGRASP efficiently generates natural human grasps aligned with linguistic intentions. The method is evaluated using metrics such as physical plausibility and semantic consistency. It outperforms existing methods in these metrics. The method is applied in AR/VR and embodied robotics, demonstrating the ability to synthesize dynamic grasp motions. The method's discrete representation is both interpretable and controllable, making it suitable for semantic space alignment. The method is also effective in generating grasps based on language instructions, as demonstrated by experiments. The method's contributions include the introduction of SEMGRASP, a novel grasp discrete representation, and the CAPGRASP dataset. The dataset includes low-level, high-level, and conversational annotations, making it the first of its kind. The method is trained using a VQ-VAE and an MLLM, with the VQ-VAE used for grasp discretization and the MLLM for grasp generation. The method is evaluated on multiple metrics and shows superior performance compared to existing methods. The method is also effective in applications such as AR/VR and embodied robotics, demonstrating the potential for generating more human-like, semantically coherent grasps in various contexts. Limitations include the need for further exploration in two-hand manipulation and end-to-end semantic grasp motion synthesis.