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This paper begins with a review of the history of remote sensing algorithms for the determination of particulate inorganic carbon (PIC; aka calcium carbonate), primarily associated with haptophyte phytoplankton known as coccolithophores. These algae have strong optical particle backscattering (b bp) which can dominate ocean color properties.. In non-bloom conditions, coccolithophore b bp typically accounts for ∼10-20% of the total b bp , whereas in turbid coccolithophore blooms, coccolithophore b bp can account for >90% of total b bp. Since total b bp features heavily in a number of algorithms for the determination of phytoplankton standing stock, disproportionate coccolithophore b bp can cause significant errors in a wide variety of other ocean-color algorithms. Here we discriminate between qualitative coccolithophore algorithms (coccolith flags), quantitative algorithms to determine the concentration of coccolithophore PIC and algorithms that focus on coccolithophore biomass. Algorithms from satellite sensors, such as the AVHRR and MISR, not typically used for phytoplankton remote sensing, are discussed as well as an improved method to model the backscattering cross-section of PIC. We also cover remote sensing algorithms for determination of calcification rates, modeling vertical profiles of PIC for the remote sensing of integrated euphotic PIC, and the effect of coccolithophore species variation on PIC retrievals. The second part of this review paper covers what we have learned about the cycling of PIC from remotely-sensed satellite measurements since the first satellite observations in 1982. The analysis begins from the global perspective, then focuses on five sub-regions which have become notorious for their regular, high-reflectance coccolithophore blooms (Southern Ocean, Atlantic Ocean, Arctic Ocean, Black Sea and Bering Sea). We end with a discussion of future directions for the PIC algorithms using machine-learning approaches and hyperspectral applications during the upcoming PACE era. [ABSTRACT FROM AUTHOR]