Unstructured grids are extensively used in modern computational solvers and, thus, play an important role in scientific visualization. They come in many different types. One of the most general types are non-convex meshes, which may contain voids and cavities. The lack of convexity presents a problem for several algorithms, often causing performance issues. One way around the complexity of non-convex methods is to convert them into convex ones for visualization purposes. This idea was originally proposed by Peter Williams in his seminal paper on visibility ordering. He proposed to fill the volume between the convex hull of the original mesh, and its boundary with “imaginary” cells. In his paper, he sketches algorithms for potentially performing this operation, but stops short of implementing them. This paper discusses the convexification problem and surveys the relevant literature. We hope it is useful for researchers interested in the visualization of unstructured grids.