In this seminar I will present the project COOL (Cosmic Origins Of Life), which aims at elucidating to what extent the first biochemically-relevant species leading to the origin of Life could have appeared already in the interstellar medium. For this, we push the limits of Astrochemistry towards detecting in space key molecular species with increasing complexity. Our study is focused on understanding how thebuilding blocks of nucleotides (phosphates, sugars and nucleobases) can form in space. To achieve this goal, we use a multidisciplinary approach that combines astronomical observations with state-of-the-art chemical models and laboratory experiments. The final aim is to understand whether basic Biochemistry can already occur in the interstellar medium, assembling the basic pieces of DNA and RNA in outer space. This research will help us to understand how Life may have originated on Earth and on how it may appear in other planetary systems.