Harmful algal blooms (HABs) adversely impact aquatic organisms, human health, and the marine economy. The need to understand the origins and mechanisms of HAB occurrence and development determines the relevance of the study of these phenomena, including using remote sensing methods and assets. Here we present the results of a comprehensive study of conditions and precursors of some intense HABs detected in the water areas near the island of Chiloe (Chile, 2016), near the Kamchatka Peninsula (Russia, 2020), near the island of Hokkaido (Japan, 2021), among others. The study involves statistical analysis of long-term satellite and model data arrays on significant parameters of the marine environment and near-surface atmosphere, as well as empirical modeling of HAB risks. Information products on the following environmental parameters were used: sea surface temperature (SST, NOAA OISST, since 1981), the level of photosynthetically active radiation (PAR) and chlorophyll-a concentration (MODIS Ocean Color SMI, since 2000), sea surface salinity and height (HYCOM, since 1993), and near-surface wind speed and direction (NCEP CFSv2, since 1979). Quantitative assessments of the dynamics of informative criteria were applied. The key criterion is the ratio (Δσ) of the absolute deviation of the studied parameter from the expected norm to the RMS deviation of its values. Intense HABs were often preceded by excessive SST (up to Δσ ~1.99) and PAR (up to Δσ ~2.25) values, as well as low near-surface wind speed (up to Δσ ~−1.83). These environmental parameters considerably contribute to HAB generation and intensification. An approach and empirical function were proposed that allow us to assess the risk of HAB phenomena and reveal their precursors. Using the proposed approach and empirical function, the precursors of ten HABs were identified, nine of which were confirmed by in situ data. The results can be used as a tool for forecasting and studying the conditions for the occurrence of HABs, representing one of the promising directions for monitoring these dangerous phenomena.