The problem of how cooperation can evolve between individuals or entities with conflicting interests is central to biology as many of the major evolutionary transitions, from the first replicating molecules to human societies, have required solving this problem. There are many routes to cooperation but humans seem to be distinct from other species as they have more complex and diverse mechanisms, often due to their higher cognitive skills, allowing them to reap the benefits from living in groups. Among those mechanisms, the use of reputation or past experience with others as well as sanctioning mechanisms both seem to be of major importance. They have often been considered separately but the interaction between the two might provide new insights as to how punishment could have appeared as a means to enforce cooperation in early humans. In this thesis, I firstly use theoretical approaches from evolutionary game theory to investigate the evolution of punishment and cooperation through a reputation system based on punitive actions, and compare the efficacy of this system, in terms of cooperation achieved, with one based on cooperative actions. On the other hand, I use empirical approaches from economics to test, in real life, predictions from theoretical models but also to explore further conditions such as environmental variation, constrained memory, or even the scale of competition between individuals. Both approaches have allowed contributing to the understanding of how these factors affect reputation and punishment use, and ultimately how cooperation is achieved.