Organic compounds of high degree of complexity are now known to be widespread in the Universe, ranging from objects in our Solar System to distant galaxies. Through the techniques of millimeter-wave spectroscopy, over 140 molecules have been identified through their rotational transitions. Space infrared spectroscopy has detected the stretching and bending modes of compounds with aromatic and aliphatic structures. Analyses of samples of meteorites, comets, asteroids, and interplanetary dust also revealed a rich content of organic substances, some of which could be of extra-solar origin. We review the current state of understanding of the origin, evolution, nature, and distribution of organic matter in space. Also discussed are a number of unexplained astronomical phenomena whose origins could be traced to organic carriers.