Atomic-scale modeling and understanding of materials have made remarkable progress, but they are still fundamentally limited by the large computational cost of explicit electronic-structure methods such as density-functional theory. This Progress Report shows how machine learning (ML) is currently enabling a new degree of realism in materials modeling: by "learning" electronic-structure data, ML-based interatomic potentials give access to atomistic simulations that reach similar accuracy levels but are orders of magnitude faster. A brief introduction to the new tools is given, and then, applications to some select problems in materials science are highlighted: phase-change materials for memory devices; nanoparticle catalysts; and carbon-based electrodes for chemical sensing, supercapacitors, and batteries. It is hoped that the present work will inspire the development and wider use of ML-based interatomic potentials in diverse areas of materials research.