Frequent itemsets play an essential role in many data mining tasks that try to find interesting patterns from databases, such as association rules, correlations, sequences, episodes, classifiers, clusters and many more. Although the collection of all frequent itemsets is typically very large, the subset that is really interesting for the user usually contains only a small number of itemsets. Therefore, the paradigm of constraint-based mining was introduced. Constraints provide focus on the interesting knowledge, thus reducing the number of patterns extracted to those of potential interest. Additionally, they can be pushed deep inside the mining algorithm in order to achieve better performance. For this reason the problem of how to push different types of constraints into the frequent itemsets computation has been studied a lot. In this talk we will describe recent algorithmic results in pushing monotone constraints in the frequent pattern computation.