Astrochemistry aims at studying chemical processes in astronomical environments. This discipline -- located at the crossroad between astrophysics and chemistry -- is rapidly evolving and explores the issue of the formation of molecules of increasing complexity in particular physical conditions that deviate significantly from those frequently encountered in chemistry laboratories. The main goal of this paper is to provide an overview of this discipline. So far, about 170 molecules have been identified in the interstellar medium (ISM). The presence of this molecular diversity constitutes a firm evidence that efficient formation processes are at work in the interstellar medium. This paper aims at summarizing most of present ideas that are explored by astrochemists to investigate the chemistry taking place in various astronomical environments, with emphasis on the particular conditions which are met in space (including radiation fields, cosmic-rays, low densities...). The more ambitious question of the molecular complexity is addressed following two approaches presented to be converging. The first approach considers the growing complexity starting from the most simple chemical species in interstellar environments, and the second approach envisages successive precursors of the most complex species commonly found on Earth, and in particular in our biochemistry. The issue of molecular complexity constitutes one of the main modern scientific questions addressed by astrochemistry, and it is used as a guideline across this paper.
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