Frequent multispectral observations of sufficient spatial detail from well-calibrated spaceborne sensors are needed for large-scale terrestrial monitoring. To meet this demand, the NASA Harmonized Landsat and Sentinel-2 (HLS) project was initiated in early 2010s to produce comparable 30-m surface reflectance from the US Landsat 8 Operational Land Imager (OLI) and the European Copernicus Sentinel-2A MultiSpectral Instrument (MSI), and currently from two OLI and two MSI sensors, by applying atmospheric correction to top-of-atmosphere (TOA) reflectance, masking out clouds and cloud shadows, normalizing bi-directional reflectance view angle effects, adjusting for sensor bandpass differences with the OLI as the reference, and providing the harmonized data in a common grid. Several versions of HLS dataset have been produced in the last few years. The recent improvements on almost all the harmonization algorithms had prompted a production of a new HLS dataset, tagged Version 2.0, which was completed in the summer of 2023 and for the first time takes on a global coverage (except for Antarctica). The HLS V2.0 data record starts in April 2013, two months after Landsat 8 launch. For 2022, the first whole year two Landsat and two Sentinel-2 satellites were available, HLS provides a global median of 66 cloud-free observations over land, substantially more than from a single sensor. This paper describes the HLS algorithm improvements and assesses the harmonization efficacy by examining how the reflectance difference between contemporaneous Landsat and Sentinel-2 observations was successively reduced by each harmonization step. The assessment was conducted on 545 pairs of globally distributed same-day Landsat/Sentinel-2 images from 2021 to 2022. Compared to the TOA data, the HLS atmospheric correction slightly increased the reflectance relative difference between Landsat and Sentinel-2 for most of the spectral bands, especially for the two blue bands and the green bands. The subsequent bi-directional reflectance view angle effect normalization effectively reduced the between-sensor reflectance difference present in the atmospherically corrected data for all the spectral bands, and notably to a level below the TOA differences for the red, near-infrared (NIR), and the two shortwave infrared (SWIR) bands. The bandpass adjustment only had a modest effect on reducing the between-sensor reflectance difference. In the final HLS products, the same-day reflectance difference between Landsat and Sentinel-2 was below 4.2% for the red, NIR, and the two SWIR bands, all smaller than the difference in the TOA data. However, the between-sensor differences for the two blue and the green bands remain slightly higher than in TOA data, and this reflects the difficulty in accurately correcting for atmospheric effects in the shorter wavelength visible bands. The data consistency evaluation on a suite of commonly used vegetation indices (VI) calculated from the HLS V2.0 reflectance data showed that the between-sensor VI difference is below 4.5% for most of the indices. These results suggest that the harmonization is robust and the HLS V2.0 data are adequate for quantitative terrestrial applications.