Knowledge discovery in large and complex datasets is one main topic addressed in ``Data Science'' and as well in ``Science of Knowledge'' (i.e. Artificial Intelligence). Indeed data and knowledge are in constant interaction. Knowledge discovery is applied to datasets and has a direct impact on the design of knowledge bases (ontologies). Dually, the declarative principles supporting knowledge representation can be reused in knowledge discovery, leading to the recent idea of ``declarative data mining'', i.e. specify the problem and let the solver do what should be done. Actually, diversity, complexity and size of the data are current challenges in Knowledge Discovery. Accordingly, it could be interesting to have at hand a generic formalism based on declarative principles and supporting the interplays between data and knowledge and between discovery and representation. In this presentation, we will introduce firstly ``Exploratory Knowledge Discovery'' and then Formal Concept Analysis (FCA) and its extension, namely ``pattern structures''. FCA is a mathematical formalism for data and knowledge processing. FCA starts with a binary table composed of objects and attributes and outputs a concept lattice. In a concept lattice, each concept is made of an intent (i.e. the description of the concept in terms of attributes) and an extent (i.e. the objects instances of the concept). Intents and extents are two dual facets of a concept that naturally apply in knowledge representation. Moreover, the structure of a concept lattice (or part of it) can be visualized and allows a suggestive interpretation for human agents while being also processable by software agents. Afterward, we will show how FCA and especially pattern structures satisfy requirements of exploratory knowledge discovery. Pattern structures are able to process various complex data, e.g. numbers, sequences, trees, and graphs. Finally, we will discuss a series of tasks in which pattern structures were successfully applied, e.g. text mining, information retrieval, biclustering, recommendation, concept definition mining and discovery of functional dependencies.