Image watermarking methods are not tailored to handle small watermarked areas. This restricts applications in real-world scenarios where parts of the image may come from different sources or have been edited. We introduce a deep-learning model for localized image watermarking, dubbed the Watermark Anything Model (WAM). The WAM embedder imperceptibly modifies the input image, while the extractor segments the received image into watermarked and non-watermarked areas and recovers one or several hidden messages from the areas found to be watermarked. The models are jointly trained at low resolution and without perceptual constraints, then post-trained for imperceptibility and multiple watermarks. Experiments show that WAM is competitive with state-of-the art methods in terms of imperceptibility and robustness, especially against inpainting and splicing, even on high-resolution images. Moreover, it offers new capabilities: WAM can locate watermarked areas in spliced images and extract distinct 32-bit messages with less than 1 bit error from multiple small regions -- no larger than 10% of the image surface -- even for small 256x256 images. Training and inference code and model weights are available at https://github.com/facebookresearch/watermark-anything.