The Universe is a naturally hierarchical place, with objects and systems at a range of physical scales. In astronomy, these include planets, stars, supermassive black holes, stellar clusters, galaxies, galaxy clusters, and the greater cosmic web of dark matter. Many of these objects and systems provide unique opportunities to test physics in extreme environments that are difficult or impossible to replicate in the lab. However, the use of astronomical data presents many challenges, including incompleteness, selection bias, and the translation and interpretation of data to physical quantities, among others. Hierarchical Bayesian techniques are an increasingly popular framework within which to study astronomical objects and systems because they can help to overcome some of these challenges. In this talk, I will provide an introduction to the hierarchical Universe and place in the astronomical context the four following talks about applications and developments of Bayesian statistics. We hope that this introductory lecture and the rest of the talks in the session "Hierarchical Bayes in a Hierarchical Universe" will encourage you to get involved with an astrostatistics project!