Résumé : As a consequence of globalization, interactions among countries, companies, people, etc, have been increased during recent decades. The basic mathematical support structure for modeling such interactions is a network. Thus, Network Design plays an important role for facilitating the interactions. Nevertheless, %Network Design Problems have been studied since the interest of modelling the interaction between a set of individuals became to gain importance. Nevertheless, the majority of Network Design problems are difficult to solve. Our goal is to study them from the Combinatorial Optimization point of view to find exact and metaheuristic \mbox{approaches} that improve the process of getting optimal ,or at least good, solutions for practical applications. In this thesis, we study some Network Design problems, which can be grouped into two large classes detailed below, according to the main feature of each one. In all the problems it is considered that the demand is given by a set of pairs of origin-destination points. That is, each demand has to move from an origin-node to a destination-node. Another feature in common is the existence of an alternative network that can be used by the demand set. In this situation, the possible existing competition between the network to be designed and the already actual alternative network has been highlighted. On the one hand, Chapters 2, 3 and 4 deal with Covering Network Design \mbox{problems}. These problems seek to design a network in such a way that the proportion of demand covered is maximized or exceeds a certain percentage of the total. Particularly, the third chapter shows a practical application for Network Design in the transportation area. On the other hand, Chapter 5 extends the existing notions in Facility Location Theory of $\lambda$-Cent-Dian and Generalized-Center to the area of Network Design. The problems in this chapter are focused on designing a network that minimizes the maximum distance of a known set of origin-destination pairs (within that network), the average distance, a linear combination of both objectives or the difference between them. These objectives may be of interest for some of the needs at the present time.All problems are approached from the standpoint of Mathematical Programming. Each of them has been described in detail and some properties have been found. Then, formulations have been proposed. Afterwards, from a computational perspective, preprocessing methods have been developed before focusing on the resolution procedures.The research done can also be grouped by the nature of the resolution methods used to tackle the problems proposed. On the one hand, some stabilizations for the Benders decomposition method have been developed. On the other hand, metaheuristic approaches have been also considered for some of the problems concerned. In this situation, Greedy Randomized Adaptive Search Procedures and a Genetic Algorithm elaborated by other authors are evaluated. Furthermore, we have developed a Simulated Annealing and an Adaptive Large Neighborhood Search routine.