Robust lossless data hiding (LDH) methods have attracted more and more attentions for copyright protection of multimedia in lossy environment. One of the important requirements of the robust LDH methods is the reversibility, that is, the host images can be recovered without any distortion after the hidden messages are removed. The reversibility is often guaranteed by the embedding model, which affects the performance of the methods greatly. Another requirement is to have a better robustness, which allows the LDH methods to be well adaptable to the lossless and lossy environment, e.g., JPEG compression. In this paper, we firstly categorize the existing robust LDH methods according to the embedding model, and then make a theoretical analysis on the performance in terms of capacity, invisibility and the robustness. Finally, experimental comparisons are carried out to summarize the advantages and disadvantages of each kind of method.