Remote sensing of solar-induced chlorophyll fluorescence (SIF) is a rapidly advancing front in terrestrial vegetation science, with emerging capability in space-based methodologies and diverse application prospects. Although remote sensing of SIF – especially from space – is seen as a contemporary new specialty for terrestrial plants, it is founded upon a multi-decadal history of research, applications, and sensor developments in active and passive sensing of chlorophyll fluorescence. Current technical capabilities allow SIF to be measured across a range of biological, spatial, and temporal scales. As an optical signal, SIF may be assessed remotely using high-resolution spectral sensors in tandem with state-of-the-art algorithms to distinguish the emission from reflected and/or scattered ambient light. Because the red to far-red SIF emission is detectable non-invasively, it may be sampled repeatedly to acquire spatio-temporally explicit information about photosynthetic light responses and steady-state behaviour in vegetation. Progress in this field is accelerating with innovative sensor developments, retrieval methods, and modelling advances. This review distills the historical and current developments spanning the last several decades. It highlights SIF heritage and complementarity within the broader field of fluorescence science, the maturation of physiological and radiative transfer modelling, SIF signal retrieval strategies, techniques for field and airborne sensing, advances in satellite-based systems, and applications of these capabilities in evaluation of photosynthesis and stress effects. Progress, challenges, and future directions are considered for this unique avenue of remote sensing.