The emerging technique of remotely sensed sun-induced fluorescence (SIF) offers great advantages for estimating the gross primary photosynthetic (GPP) and investigating carbon cycles at regional and global scales. This novel satellite product is a state-of-the-art and booming avenue in recent years. Particularly, the flourishing progressions in retrieval techniques, vegetation monitoring, and applications in carbon cycle model have been accelerated to implement a satellite-based inversion at a global scale since 2011. During photosynthesis, part of solar radiation absorbed by chlorophyll is re-emitted at long wavelengths (fluorescence). Chlorophyll fluorescence is an electromagnetic emission in the 650-800 nm range originating at the core of the photosynthetic machinery. It been used in leaf-scale studies of photosynthesis in laboratory conditions for several decades. By using new, high-resolution spectrometers, chlorophyll fluorescence can be readily retrieved from satellite platforms. This scheme can be used to quantify the photosynthetic activity and efficiency globally. Satellite observations of chlorophyll fluorescence are important to reduce the uncertainties in research of global carbon cycle and climate change. In this review, we introduced the recent development in the remote sensing of SIF. First, recent instrumental and methodological developments in the field of spaceborne spectroscopy have rendered the measurement of SIF from space possible, which can alleviate the current limitations for the monitoring of terrestrial photosynthesis. Since 2011, the global data of SIF have been retrieved from a series of spaceborne instruments providing high-resolution spectra, such as the GOSAT's Fourier transform spectrometer, ENVISAT/SCIAMACHY, MetOp-A/GOME-2, and OCO-2. The spatial coverage and resolution, wavelength, acquisition time, and amount of data available for analysis depend on the instrument from which they are derived. As a complement to reflectance-based vegetation indices, SIF offers new possibilities to monitor photosynthesis and GPP of terrestrial ecosystem from space. The potential of SIF, which is an indicator of large-scale GPP, has been demonstrated in a relatively short life time of global SIF data. Recent studies have shown that satellite observations of SIF are an excellent proxy for GPP at canopy and ecosystem scales. Meanwhile, spaceborne SIF data have also been used to monitor large-scale vegetation status in drought conditions, thereby suggesting that SIF provides unique, perhaps most direct, information from space for early warning and accurate monitoring of emerging drought. The potential of SIF as a constraint on regional and global carbon cycle variations has also been demonstrated together with the XCO_2 data from GOSAT and OCO-2. Despite this experimental evidence of a direct and linear correlation between spatio-temporal aggregates of remotely sensed SIF data and large-scale GPP, the relationship between instantaneous photosynthesis and SIF is relatively complicated. Further study is necessary to investigate how the remotely sensed SIF signal can be used for plant photosynthesis monitoring, how we can interpret the SIF signal at various spatial and temporal scales, and how we link the active PAM measurements with canopy SIF at the seasonal scale. At the end of this review, we proposed a number of areas where further research can be conducted to better understand the mechanisms that govern the seasonality of canopy- and leaf-level SIF signal and its relation with photosynthesis. Several prospective areas for future work include improving the accuracy of retrievals with additional data, characterizing the mechanistic relationship between SIF and GPP across scales, measurements of near-surface continuous SIF along with eddy covariance flux system, data assimilation of SIF into land surface models, and development of new index for stress detection from SIF.