This book describes some of the frontier problems of cosmology: our almost total ignorance of what the Universe is made up of, the mystery of its origin and its end. The book starts with a description of the historical events that led to the construction of the Big Bang model together with the stages that transformed the Universe from a very hot place to a very cold one, full with the structures that we observe today. These structures (stars, galaxies, etc.) constitute only 5% of the contents of the Universe. Concerning the remaining 95%, dubbed dark matter and dark energy, we know very little, and we have only indirect evidence of their existence. The text describes the story and the protagonists who showed the need for the existence of this 'missing matter', the observations, and puzzles they had to solve to understand that dark matter was not ordinary matter. The book describes the hunt for dark matter, carried out with instruments operating in space, on the Earth's surface, and in laboratories built in the bowels of the Earth. It also describes dark energy, which manifests itself in the accelerated expansion of the Universe, and appeared only a few billions of years ago. The book discusses why dark energy must exist and what its existence implies, especially for the future and the end of our Universe.