Lossless data embedding has the property that the distortion due to embedding can be completely removed from the watermarked image without accessing any side channel. This can be a very important property whenever serious concerns over the image quality and artifacts visibility arise, such as for medical images, due to legal reasons, for military images or images used as evidence in court that may be viewed after enhancement and zooming. We formulate two general methodologies for lossless embedding that can be applied to images as well as any other digital objects, including video, audio, and other structures with redundancy. We use the general principles as guidelines for designing efficient, simple, and high-capacity lossless embedding methods for three most common image format paradigms - raw, uncompressed formats (BMP), lossy or transform formats (JPEG), and palette formats (GIF, PNG). We close the paper with examples of how the concept of lossless data embedding can be used as a powerful tool to achieve a variety of non-trivial tasks, including elegant lossless authentication using fragile watermarks. Note on terminology: some authors coined the terms erasable, removable, reversible, invertible, and distortion-free for the same concept.