Large Multimodal Models (LMMs) extend Large Language Models to the vision domain. Initial LMMs used holistic images and text prompts to generate ungrounded textual responses. Very recently, region-level LMMs have been used to generate visually grounded responses. However, they are limited to only referring to a single object category at a time, require users to specify the regions in inputs, or cannot offer dense pixel-wise object grounding. In this work, we present Grounding LMM (GLaMM), the first model that can generate natural language responses seamlessly intertwined with corresponding object segmentation masks. GLaMM not only grounds objects appearing in the conversations but is flexible enough to accept both textual and optional visual prompts (region of interest) as input. This empowers users to interact with the model at various levels of granularity, both in textual and visual domains. Due to the lack of standard benchmarks for the novel setting of visually Grounded Conversation Generation (GCG), we introduce a comprehensive evaluation protocol with our curated grounded conversations. Our proposed GCG task requires densely grounded concepts in natural scenes at a large-scale. To this end, we propose a densely annotated Grounding-anything Dataset (GranD) using our proposed automated annotation pipeline that encompasses 7.5M unique concepts grounded in a total of 810M regions available with segmentation masks. Besides GCG, GLaMM also performs effectively on several downstream tasks, e.g., referring expression segmentation, image and region-level captioning and vision-language conversations. Our codes, data and models will be publicly released.