A hypergraph is a complex data structure capable of expressing associations among any number of data entities. Overcoming the limitations of traditional graphs, hypergraphs are useful to model real-life problems. Frequent pattern mining is one of the most popular problems in data mining with a lot of applications. To the best of our knowledge, there exists no flexible pattern mining framework for hypergraph databases decomposing associations among data entities. In this article, we propose a flexible and complete framework for mining frequent patterns from a collection of hypergraphs. To discover more interesting patterns beyond the traditional frequent patterns, we propose frameworks for weighted and uncertain hypergraph mining also. We develop three algorithms for mining frequent, weighted, and uncertain hypergraph patterns efficiently by introducing a canonical labeling technique for isomorphic hypergraphs. Extensive experiments have been conducted on real-life hypergraph databases to show both the effectiveness and efficiency of our proposed frameworks and algorithms.