Thompson Sampling (TS) is an efficient method for virtual screening of ultralarge synthesis on-demand databases, which have grown to tens of billions of molecules. TS is an active learning approach that streamlines the virtual screening process by performing a probabilistic search in the reagent space, eliminating the need for full enumeration of the library. The method is applicable to various virtual screening modalities, including 2D and 3D similarity searches, docking, and machine learning models. In an illustrative example, TS identified more than half of the top 100 molecules from a docking-based virtual screen of 335 million molecules by evaluating only 1% of the dataset. The article discusses the methodology, results, and comparisons with other methods, highlighting the advantages and limitations of TS. TS is particularly useful for combinatorial libraries where the library chemistry and building blocks are known, and it can significantly reduce the computational and resource requirements compared to exhaustive methods.Thompson Sampling (TS) is an efficient method for virtual screening of ultralarge synthesis on-demand databases, which have grown to tens of billions of molecules. TS is an active learning approach that streamlines the virtual screening process by performing a probabilistic search in the reagent space, eliminating the need for full enumeration of the library. The method is applicable to various virtual screening modalities, including 2D and 3D similarity searches, docking, and machine learning models. In an illustrative example, TS identified more than half of the top 100 molecules from a docking-based virtual screen of 335 million molecules by evaluating only 1% of the dataset. The article discusses the methodology, results, and comparisons with other methods, highlighting the advantages and limitations of TS. TS is particularly useful for combinatorial libraries where the library chemistry and building blocks are known, and it can significantly reduce the computational and resource requirements compared to exhaustive methods.