Reconstruction of a 3-D object surface from sample of points has a wide range of applications such as Computer-Aided Design (CAD) design, medical imaging, virtual reality and movie industry. The problem of approximating a surface from a given set of sample is known as surface reconstruction. This paper reviews the well-known algorithms used to reconstruct the topology surface from sample points in three dimensional spaces. The sample points can be obtained from photogrammetric technique, laser scanner or any other mathematical function. Generally, the sample points will describe the shape and topology surface of the object.