The Rent-or-Buy Network Design problem is a fundamental connectivity-related network design problem. The problem captures the "economies of scale" property, which says that the per-unit cost of installing capacity on edges of the network decreases as more capacity is installed. The Sample-Augment algorithm is a simple but powerful randomized approximation algorithm that effectively deals with the Rent-or-Buy and related problems. In this paper we systematically survey the Rent-or-Buy problem and the Sample-Augment algorithm, as well as its two analysis techniques, i.e., the cost-sharing method and the core-detouring scheme.