After its launch, the James Webb Space Telescope (JWST) will become one of the most important space mission in the history. This mid-infrared telescope will benefit from the largest collecting area mirror ever sent to the space. A set of many various instruments will allow the scientists to explore, along many other interesting observations, the dawn of the Universe at high redshifts, to observe the very first stars and galaxies as well as to look at selected exoplanets. In this article three scientific tasks are highlighted: the JWST deep field; a search for lensed very distant Pop III stars; and follow-up observations of a short gamma-ray burst with the aim to detect a kilonova counterpart.