The Interface Region Imaging Spectrograph (IRIS) has been obtaining near- and far-ultraviolet images and spectra of the solar atmosphere since July 2013. IRIS is the highest resolution observatory to provide seamless coverage of spectra and images from the photosphere into the low corona. The unique combination of near- and far-ultraviolet spectra and images at sub-arcsecond resolution and high cadence allows the tracing of mass and energy through the critical interface between the surface and the corona or solar wind. IRIS has enabled research into the fundamental physical processes thought to play a role in the low solar atmosphere such as ion-neutral interactions, magnetic reconnection, the generation, propagation, and dissipation of waves, the acceleration of non-thermal particles, and various small-scale instabilities. IRIS has provided insights into a wide range of phenomena including the discovery of non-thermal particles in coronal nano-flares, the formation and impact of spicules and other jets, resonant absorption and dissipation of Alfvénic waves, energy release and jet-like dynamics associated with braiding of magnetic-field lines, the role of turbulence and the tearing-mode instability in reconnection, the contribution of waves, turbulence, and non-thermal particles in the energy deposition during flares and smaller-scale events such as UV bursts, and the role of flux ropes and various other mechanisms in triggering and driving CMEs. IRIS observations have also been used to elucidate the physical mechanisms driving the solar irradiance that impacts Earth's upper atmosphere, and the connections between solar and stellar physics. Advances in numerical modeling, inversion codes, and machine-learning techniques have played a key role. With the advent of exciting new instrumentation both on the ground, e.g. the Daniel K. Inouye Solar Telescope (DKIST) and the Atacama Large Millimeter/submillimeter Array (ALMA), and space-based, e.g. the Parker Solar Probe and the Solar Orbiter, we aim to review new insights based on IRIS observations or related modeling, and highlight some of the outstanding challenges.