Abstract Frequent itemset mining is one of the most studied tasks in knowledge discovery. It is often reduced to mining the positive border of frequent itemsets, i.e. maximal frequent itemsets. Infrequent itemset mining, on the other hand, can be reduced to mining the negative border, i.e. minimal infrequent itemsets. We propose a generic framework based on constraint programming to mine both borders of frequent itemsets. One can easily decide which border to mine by setting a simple parameter. For this, we introduce two new global constraints, FREQUENTSUBS and INFREQUENTSUPERS, with complete polynomial propagators. We then consider the problem of mining borders with additional constraints. We prove that this problem is coNPhard, ruling out the hope for the existence of a single CSP solving this problem (unless coNP ? NP).