As magma rises in volcanic systems, volatile species exsolve from the silicate melt and are emitted as gases into the atmosphere. Measuring the magnitude and composition of gas emissions from volcanoes provides insights into processes occurring deep within the Earth and helps constrain the impact of volcanic degassing on atmospheric chemistry. Optical remote sensing techniques allow volcanic gas emissions to be characterized without the need to access hazardous areas near active volcanic vents. This paper reviews the state of the art in ultraviolet and visible volcanic gas remote sensing from the ground, air, and space. Special attention is given to discussing the physics of atmospheric radiative transfer on which these techniques are based. The functionality and limitations of different remote sensing instruments are examined, making clear that the ideal choice of instrumentation will depend on the volcanic system to which it is applied and the sought measurement parameters. Common algorithms for determining trace gas column densities, gas burdens, and volcanic emission rates from measurements of spectral radiance are outlined and compared, showing how some algorithms attempt to model the physics of the measurement while others maximize sensitivity. Several examples demonstrate how remote sensing measurements continue to advance our understanding of volcanic systems and their impact on the atmosphere. Finally, a few promising directions of inquiry are suggested that could lead to improvements in remote sensing instrumentation and analysis techniques. By combining spectroscopic and imaging techniques, improving our understanding of atmospheric radiative transfer, expanding the suite of target gases, and increasing the coverage and frequency of observations, we stand to significantly improve our ability to detect and quantify volcanic gas emissions and gain new insights into important Earth-system processes.