Realizing the full potential of interconnecting the large amounts of data created in physics experiments, phenomenological models and theory simulations requires robust tools for statistical inference. Here I review a particularly promising branch, Bayesian statistics, which over the past decade has found manifold use in high-energy physics. After a brief introduction to Bayesian statistics I will present two concrete examples, where Bayesian thinking has led to progress in understanding strongly interacting matter: unfolding problems in the form of lattice QCD spectral functions (in spirit similar to detector corrections), as well as the efficient estimation of quark-gluon-plasma parameters from a systematic comparison of experimental heavy-ion collision data and phenomenological models.