Topology Optimization (TO) methods for fracture resistance offer new possibilities for designing stronger structures or materials with lower masses than conventional designs. This article presents an overview of topology optimization techniques for fracture resistance, from pioneering works to the most recent developments at the time of writing. We first review stress-based methods, which were the forerunners of crack resistance methods, producing optimal designs that prevent any damage or crack initiation. Other works followed, taking into account the presence of defects or cracks in structures, but using classical approaches aimed at minimizing compliance in an elastic framework. TO methods for fatigue damage are also an important branch of these approaches and are reviewed. We then present more recent methodologies, including non-linear effects in structural design, such as plasticity and damage. Finally, we describe the latest methods of TO design for fracture resistance, including an explicit description of crack propagation during loading, from initiation to failure of structures and materials. In particular, the design of two-phase materials that are more resistant to cracking and that can be manufactured by 3D printing is discussed. The article concludes with some challenges and promising avenues for the coming years in this field.