Topological structure plays an important role in simplification

transformation

surface reconstruction

compression and transmission

matching and retrieval

shape analysis and understanding

and applications of point cloud data. It is one class of the key characters of 3D point cloud data. Relevant concepts

methods and techniques of topologically structural representation and computation are surveyed and summarized in this paper. Typical techniques and their latest developments are remarked. Practical applications of topologically structural representation and computation of point cloud data and our some latest results are presented. Our perspectives of these problems and techniques are shown.