We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {c e } on the edges, a set of facilities F ⊆ V , and a set of clients D ⊆ V . Facility i has a facility opening cost f i and client j has d j units of demand. We are also given a parameter M ≥ 1. A solution opens some facilities, say F , assigns each client j to an open facility i(j), and connects the open facilities by a Steiner tree T . The total cost incurred is i∈F f i + j∈D d j c i(j)j + M e∈T c e . We want a solution of minimum cost.A special case of this problem is when all opening costs are 0 and facilities may be opened anywhere, i.e., F = V . If we know a facility v that is open, then the problem becomes a special case of the singlesink buy-at-bulk problem with two cable types, also known as the rent-or-buy problem.We give the first primal-dual algorithms for these problems and achieve the best known approximation guarantees. We give a 8.55-approximation algorithm for the connected facility location problem and a 4.55-approximation algorithm for the rent-or-buy problem. Previously the best approximation factors for these problems were 10.66 and 9.001 respectively [8]. Further, these results were not combinatorial -they were obtained by solving an exponential size linear programming relaxation. Our algorithm integrates the primal-dual approaches for the facility location problem [11] and the Steiner tree problem [1,3]. We also consider the connected k-median problem and give a constant-factor approximation by using our primal-dual algorithm for connected facility location. We generalize our results to an edge capacitated variant of these problems and give a constant-factor approximation for these variants.