Concerns about market power and competition in the agri-food sector are widespread, with commentators regularly suggesting that farmers are in a structurally weaker position than other actors, who therefore benefit at their expense. The evidence reviewed in this paper indicates that downstream segments of agri-food chains are indeed typically more concentrated than farm-level production. Nevertheless, while competition problems were found in some instances, the current evidence does not support the claim that stronger actors in the chain systematically abuse their stronger position at the expense of farmers. An in-depth understanding of how value chains are organised is essential, as many widely used indicators provide little relevant information. In many areas, further research would be welcome, as current evidence does not cover all countries and sectors equally well.