Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Gerardo Gómez Muntané[en] Asteroids are of strategic importance for science in an effort to uncover the formation, evolution and composition of the Solar System. Near-Earth objects (NEOs) are of particular interest because of their accessibility from Earth. In this work, we will study the mathematical models, methods and techniques needed to design an asteroid retrieval. This line of research has multiple aplications, such as mitigating the hazard posed by an asteroid impact; or the obtention of resources via asteroid mining. We will analise some dynamical models used to envisage an asteroid orbit. We will take profit of the dynamics of these models to minimize the required energy to perform an asteroid capture. Different transfer techniques in each of these models will be shown. At last, we will explain the whole process behind an asteroid retrieval: from the asteroids database selection, to the construction and posterior refinement of the transfer trajectory.