3D meshes are commonly used to represent virtual surface and volumes. However, their raw data representations take a large amount of space. Hence, 3D mesh compression has been an active research topic since the mid 1990s. In 2005, two very good review articles describing the pioneering works were published. Yet, new technologies have emerged since then. In this article, we summarize the early works and put the focus on these novel approaches. We classify and describe the algorithms, evaluate their performance, and provide synthetic comparisons. We also outline the emerging trends for future research.