Long-range van der Waals (vdW) or dispersion interactions are crucial in determining the structure, stability, and function of many systems throughout the fields of biology, chemistry, physics, and materials science. In this work, I will discuss several first-principles based approaches that have been recently developed for obtaining an accurate theoretical description of vdW interactions in molecules and materials. Particular focus will be placed on the many-body dispersion (MBD) model, which includes both long-range Coulomb electrodynamic response screening effects as well as a treatment of the many-body vdW energy to infinite order. To demonstrate the increasingly important role played by many-body vdW interactions in large, structurally complex molecular systems, this method will be used to investigate several pertinent molecular properties, such as binding energies/affinities in gas-phase molecular dimers and supramolecular complexes, relative conformational energetics in small polypeptides and DNA helices, anomalous structural and density signatures of liquid water, and thermodynamic stabilities among competing molecular crystal polymorphs.