Given a point set S ∈ R^d sampled from an unknown object O, the reconstruction problem is to unveil the shape of the object which best approximates O. The problem has an irrefutable place in many fields such as computer graphics, computer vision, pattern recognition, GIS (geographical information systems), and computational geometry, among others. In this talk, we discuss simple and efficient reconstruction algorithms for 2D & 3D point sets using local and global Delaunay triangulation. We start with a unified algorithm, designed for simple closed curves. Later, we discuss an algorithmic framework with three modules (discernment, shape reconstruction, and curve reconstruction). The discernment module computes the type of point set (whether it is a boundary sample or not) and then it triggers the corresponding reconstruction module which in turn reconstructs both the outer boundary and inner boundary (hole) in a single pass. Finally, a local Delaunay-based surface reconstruction algorithm is presented.