In recent years, the Topological Optimization method has noted a great progress. In its application, material is removed from an originally set geometry in order to save material, time and minimize the mass of the object without altering its static function. The Topological Optimization method is gaining increasing interest in the world of architectural design, being referred in a variety of articles and studies. This research paper is about Topological Optimization of objects, their manufacture through Additive Manufacturing and the application of their combination in Architecture.  Initially, the paper introduces the concepts of Optimization, Topological Optimization and Additive Manufacturing, and highlights the suitability of using Additive Manufacturing for topologically optimized objects, due to the complexity of their geometry and the difficulty of their construction by conventional methods. Moreover, examples of the application of Topological Optimization are presented, starting from the smallest scale, in which nodes of structures and mechanical elements are located, to the larger scales, which include structural and building elements. Some conclusions are drawn from the study of the examples, regarding the scale and construction of objects, the use of Topological Optimization as a design tool and the relationship between architectural and engineering design.  In addition, some of the most well-known software using Topological Optimization are presented, along with a study to find which are the most suitable for architectural design. Finally, the theoretical research is framed by some experimental bridge models in which Topological Optimization was used. One of the three-dimensional, topologically optimized, models was chosen to be produced by the Additive Manufacturing method to conclude the research work.