Magnetic reconnection is a fascinating effect in which magnetic field lines in plasmas counterintuitively break. This process converts energy stored in magnetic fields into kinetic and thermal energy of the surrounding plasma, and it often occurs explosively. It was discovered in the 1940s and 50s in the context of solar flares, but is now known or expected to play an important role in many settings: the solar corona (coronal mass ejections, coronal heating, etc.) and the coronae of other stars, the Earth's magnetosphere (magnetic substorms, coupling of the solar wind to the magnetosphere) and other planetary magnetospheres, fusion devices (disruptions and sawtooth phenomena), and many astrophysical settings. Therefore, reconnection is a critical component of the seemingly disparate topics of renewable energy and space weather, which has experienced wide-scale media attention of late. Despite being known for over 60 years, it remains a grand challenge problem in plasma physics; its difficulty arises because it requires an understanding of effects on multiple spatial and temporal scales. In this talk, results from analytic theory and large-scale numerical simulations will be presented. Particular examples include: (1) a discussion of which of a number of forms of reconnection likely play a role in solar flares, which is important for understanding energy accumulation before flares and their explosive onset, (2) the nature and cause of so-called supra-arcade downflows (or tadpoles) which is important for understanding how energy in solar flares is released, and (3) a summary of recent work on how reconnection between two disparate plasmas proceeds, which is important for determining the efficiency of solar wind-magnetospheric coupling at the dayside of the Earth's magnetosphere for space weather applications. For each example, observational consequences will be stressed.