Reputational concerns are believed to play a crucial role in explaining cooperative behaviour among non-kin humans. Individuals cooperate to avoid a negative social image if being branded as defector reduces pay-offs from future interactions. Similarly, individuals sanction defectors to gain a reputation as punisher, prompting future co-players to cooperate. But reputation can only effectively support cooperation if a sufficient number of individuals condition their strategies on their co-players' reputation, and if a sufficient number of group members are willing to record and transmit the relevant information about past actions. Using computer simulations, this paper argues that starting from a pool of non-cooperative individuals, a reputation system based on punishment is likely to emerge and to be the driver of the initial evolution of cooperative behaviour. However, once cooperation is established in a group, it will be sustained mainly through a reputation mechanism based on cooperative actions.