We describe our effort to produce the first-ever near-real-time (NRT) global daily chlorophyll-a (Chl-a) anomaly products that can be used to detect and identify algae blooms from satellite ocean color measurements such as those from the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard the Suomi National Polar-orbiting Partnership (SNPP) and NOAA-20. Specifically, the production of the two Chl-a anomaly products, one for the Chl-a anomaly in difference and another for the Chl-a anomaly ratio (or in its relative difference) compared to the 61-day Chl-a median value from the previous time period (as a Chl-a reference), has been implemented in the daily global NRT satellite data processing. These two Chl-a anomaly products represent the global ocean and coastal/inland water Chl-a abnormal condition for a given location and can provide more complete characteristics for the daily phytoplankton (or algae) biomass status by comparing to the normal condition. Detailed satellite Chl-a anomaly algorithms, the implementation of the algorithms in the routine satellite data processing, and the global data processing procedure are described and discussed. In addition, we provide several specific examples from the VIIRS-measured global daily Chl-a anomaly products to demonstrate various applications in the detection of algae blooms, including the harmful algal blooms (HABs), in various ocean and coastal/inland waters. Some quantitative seasonal and interannual evaluations and characterizations of Chl-a anomalies over global oceans and several coastal/inland waters are also provided and discussed.