We are designing new data mining techniques on boolean contexts to identify a priori interesting bi-sets, i.e., sets of objects (or transactions) and associated sets of attributes (or items). It improves the state of the art in many application domains where transactional/boolean data are to be mined (e.g., basket analysis, WWW usage mining, gene expression data analysis). The so-called (formal) concepts are important special cases of a priori interesting bi-sets that associate closed sets on both dimensions thanks to the Galois operators. Concept mining in boolean data is tractable provided that at least one of the dimensions (number of objects or attributes) is small enough and the data is not too dense. The task is extremely hard otherwise. Furthermore, it is important to enable user-defined constraints on the desired bi-sets and use them during the extraction to increase both the efficiency and the a priori interestingness of the extracted patterns. It leads us to the design of a new algorithm, called D-Miner, for mining concepts under constraints. We provide an experimental validation on benchmark data sets. Moreover, we introduce an original data mining technique for microarray data analysis. Not only boolean expression properties of genes are recorded but also we add biological information about transcription factors. In such a context, D-Miner can be used for concept mining under constraints and outperforms the other studied algorithms. We show also that data enrichment is useful for evaluating the biological relevancy of the extracted concepts.