The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lovász (1974) and Mader (1978) showed the existence of this operation while preserving global and local connectivities respectively in graphs under mild conditions. In this talk, I will introduce a splitting-off operation in hypergraphs. Main results are that there exists a local connectivity preserving complete splitting-off in hypergraphs and a strongly polynomial-time algorithm to compute it in weighted hypergraphs. If time permits, I will illustrate the usefulness of our splitting-off operation in hypergraphs by showing two applications: (1) constructive characterization of k-hyperedge-connected hypergraphs and (2) alternate proof of an approximate min-max relation for max Steiner rooted-connected orientation of graphs and hypergraphs (due to Király and Lau (Journal of Combinatorial Theory, 2008)). Our proof of the approximate min-max relation for graphs circumvents the Nash-Williams' strong orientation theorem and uses tools developed for hypergraphs. Based on joint work with Kristof Berczi, Tamas Kiraly, and Shubhang Kulkarni.