In the past decade, Astrochemistry has witnessed an impressive increase in the number of detections of complex organic molecules. Some of these species are of prebiotic interest such as glycolaldehyde, the simplest sugar, or amino acetonitrile, a possible precursor of glycine. Recently, we have reported the detection of several new complex organic species in the interstellar medium, such as hydroxylamine and ethanolamine, known to be intermediate species in the formation process of ribonucleotides and phospholipids within theories for the origin of life. In this talk, I will present our recent efforts to establish whether key precursors of prebiotic systems chemistry can be found in space. I will also analyse how chemical complexity builds up in the interstellar medium thanks to observations of the complex organic content in starless/pre-stellar cores, which represent the initial conditions of Solar-system formation.