Polycrystalline materials are ubiquitous in technology, and grain boundaries have long been known to affect materials properties and performance. First principles materials modeling and electron microscopy methods are powerful and highly complementary for investigating the atomic scale structure and properties of grain boundaries. In this review, we provide an introduction to key concepts and approaches for investigating grain boundaries using these methods. We also provide a number of case studies providing examples of their application to understand the impact of grain boundaries for a range of energy materials. Most of the materials presented are of interest for photovoltaic and photoelectrochemical applications and so we include a more in depth discussion of how modeling and electron microscopy can be employed to understand the impact of grain boundaries on the behavior of photoexcited electrons and holes (including carrier transport and recombination). However, we also include discussion of materials relevant to rechargeable batteries as another important class of materials for energy applications. We conclude the review with a discussion of outstanding challenges in the field and the exciting prospects for progress in the coming years.