The growth of small disturbances and the subsequent transition from laminar to turbulent flow is of central importance in many engineering applications, including high-speed flight, inertial confinement fusion, and noise pollution from airplanes and wind turbines. The growth of disturbances in fluids has traditionally been characterized by their long-time asymptotic stability and, more recently, by the optimal transient (finite-time) amplification maximized over all possible initial disturbances. These descriptions, while valuable, are limited in numerous ways: the asymptotic growth or decay may emerge only on unreasonably long timescales, real disturbances typically grow much less than the finite-time optimal disturbance, and both methods rely on linearized governing equations that are not always accessible. We have developed a suite of statistical and data-driven tools to overcome these limitations and provide a more comprehensive description of the growth of disturbances in fluid systems. Given a statistical description of the initial disturbances, our framework predicts the expected (mean) growth, a hierarchy of coherent structures responsible for the expected growth, and the probability of observing any particular level of amplification, i.e., the probability density function of the evolved disturbances. Additionally, we have developed a data-driven implementation of the optimal transient growth theory that approximates the upper bound on the growth of any initial disturbance given finite data. We are currently using these new tools to develop a probabilistic transition model for hypersonic boundary layers and to assess the impact of surface imperfections of fuel capsules for inertial confinement fusion.