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This review is concerned with the formation of molecules in the interstellar medium (ISM), which is composed mainly of regions of gas and dust known as interstellar clouds, ranging in size from a few to 100’s of light years in extent. Upwards of 200 different molecules have been observed spectroscopically in these objects, with a significant fraction of them ‘large’ by astronomical standards; i.e. containing six or more atoms. Interstellar clouds are of interest to chemists because of the exotic molecules and chemistry that occur in these sources, while they are of interest to astronomers because these clouds are the only known birthplaces of new stars and extrasolar planets. The formation of stars and planets from portions of dense interstellar clouds is a complex evolutionary process with multiple stages dependent upon the mass of the collapsing object. For low-mass stars such as our sun, the process is reasonably well understood and proceeds through the following intermediate stages: cold dense cores, pre-stellar cores, hot cores, and protoplanetary discs. For high-mass stars, the process is significantly less well understood because these objects are rare and are formed through evolutionary stages that are short in duration, at least astronomically speaking. Molecules are found in all of these stages, in the gas phase and often in the solid phase, with the chemistry dependent upon the physical conditions and their history. Indeed, the many molecules detected have helped significantly to unravel much of the complexity involved in stellar and planetary formation. This review is divided into sections in which, following an introduction, we discuss the different types of chemical reactions that synthesise large molecules, starting with cold dense cores of temperature 10 K and gas density, and proceeding through the various stages of low-mass star formation through protoplanetary discs. Several other types of sources are discussed briefly. We then review some recent progress that has occurred within the last several years in improving our knowledge of the chemistry in this fast-growing and rapidly evolving field of research. We end with a brief discussion of the detailed chemical simulations employed to follow the chemistry in the various sources in the ISM. [ABSTRACT FROM AUTHOR]