Fractals have been studied in areas such as mathematics, physics, chemistry, social sciences, computing, economics and biology. Fractal networks have many interesting properties, such as recursive selfsimilarity, that are present in many real networks. In this paper we study the geometrical and topological properties of fractal networks (Sierpiński triangle, the Sierpiński carpet and the Koch snowflake). Furthermore, we establish relationships, in the fractal structures studied, between the geometric properties associated with hyperbolicity and the topological indices.