The need for mining frequent patterns in hierarchical data occurs in several application contexts: classical market basket analysis has been enriched by taking into account product assortment hierarchies, phrase analysis for text mining can be improved by using background knowlegde in form of concept hierarchies and syntactic hierarchies, and discretization of continous attributes leads to large synthetic hierarchies. Starting from a description of the different requirements of these applications, we present an overview of the state-of-the-art of algorithms for tackling this problem. Hierarchical mining algorithms can be understood as special instances in a general framework for mining algorithms for complex data, which automatically makes available several algorithmic improvements as, e.g., the use of nested prefix trees.