Chlorophyll a fluorescence (ChlF) has been used for decades to study the organization, functioning, and physiology of photosynthesis at the leaf and subcellular levels. ChlF is now measurable from remote sensing platforms. This provides a new optical means to track photosynthesis and gross primary productivity of terrestrial ecosystems. Importantly, the spatiotemporal and methodological context of the new applications is dramatically different compared with most of the available ChlF literature, which raises a number of important considerations. Although we have a good mechanistic understanding of the processes that control the ChlF signal over the short term, the seasonal link between ChlF and photosynthesis remains obscure. Additionally, while the current understanding of in vivo ChlF is based on pulse amplitude-modulated (PAM) measurements, remote sensing applications are based on the measurement of the passive solar-induced chlorophyll fluorescence (SIF), which entails important differences and new challenges that remain to be solved. In this review we introduce and revisit the physical, physiological, and methodological factors that control the leaf-level ChlF signal in the context of the new remote sensing applications. Specifically, we present the basis of photosynthetic acclimation and its optical signals, we introduce the physical and physiological basis of ChlF from the molecular to the leaf level and beyond, and we introduce and compare PAM and SIF methodology. Finally, we evaluate and identify the challenges that still remain to be answered in order to consolidate our mechanistic understanding of the remotely sensed SIF signal.