Designing materials with target properties requires a deep understanding of equilibrium and non-equilibrium processes involved in synthesis, manufacturing and operation. We present examples of materials design for energy production, energy storage, and electronics. The methodology involves experimental, theoretical and computational methods that operate at various length and time scales and high performance computer simulations of coupled heat transport and chemical diffusion. To analyze the experimental and computational data, we use machine learning algorithms and a Bayesian method that accounts for different types of thermodynamic data and delivers uncertainty intervals. The presentation ends with a discussion of the emerging role of artificial intelligence in materials design.