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Recent advances in prompt learning have allowed users to interact with artificial intelligence (AI) tools in multi-turn dialogue, enabling an interactive understanding of images. However, it is difficult and inefficient to deliver information in complicated remote sensing (RS) scenarios using plain language instructions alone, which would severely hinder deep comprehension of the latent content in imagery. Besides, existing prompting strategies in natural scenes are hard to apply to interpret the RS data due to significant domain differences. To address these challenges, the first visual prompting-based multi-modal large language model (MLLM) named EarthMarker is proposed in the RS domain. EarthMarker is capable of interpreting RS imagery at the image, region, and point levels by levering visual prompts (i.e., boxes and points). Specifically, a shared visual encoding method is developed to establish the spatial pattern interpretation relationships between the multi-scale representations of input images and various visual prompts. Subsequently, the mixed visual-spatial representations are associated with language instructions to construct joint prompts, enabling the interpretation of intricate content of RS imagery. Furthermore, to bridge the domain gap between natural and RS data, and effectively transfer domain-level knowledge from natural scenes to the RS domain, a cross-domain learning strategy is developed to facilitate the RS imagery understanding. In addition, to tackle the lack of RS visual prompting data, a dataset named RSVP featuring multi-modal multi-granularity visual prompts instruction-following is constructed. Our code and dataset are available at https://github.com/wivizhang/EarthMarker.