Sentinel-2 is a very new programme of the European Space Agency (ESA) that is designed for fine spatial resolution global monitoring. Sentinel-2 images provide four 10 m bands and six 20 m bands. To provide more explicit spatial information, this paper aims to downscale the six 20 m bands to 10 m spatial resolution using the four directly observed 10 m bands. The outcome of this fusion task is the production of 10 Sentinel-2 bands with 10 m spatial resolution. This new fusion problem involves four fine spatial resolution bands, which is different to, and more complex than, the common pan-sharpening fusion problem which involves only one fine band. To address this, we extend the existing two main families of image fusion approaches (i.e., component substitution, CS, and multiresolution analysis, MRA) with two different schemes, a band synthesis scheme and a band selection scheme. Moreover, the recently developed area-to-point regression kriging (ATPRK) approach was also developed and applied for the Sentinel-2 fusion task. Using two Sentinel-2 datasets released online, the three types of approaches (eight CS and MRA-based approaches, and ATPRK) were compared comprehensively in terms of their accuracies to provide recommendations for the task of fusion of Sentinel-2 images. The downscaled ten-band 10 m Sentinel-2 datasets represent important and promising products for a wide range of applications in remote sensing. They also have potential for blending with the upcoming Sentinel-3 data for fine spatio-temporal resolution monitoring at the global scale.