This paper is a review dealing with the organic chemistry of comets. It describes how the chemical composition of comets can provide information about the chemistry of the interstellar medium, and the formation of the solar system. We discuss to what extent they could have brought to Earth the ingredients essential to the emergence of life: water and prebiotic compounds. We review all molecules which have been detected or tentatively detected in comets by remote sensing or in-situ observations, inputs of theoretical models, and all other organic species expected to be present from the results of experimental simulations. This compilation yields a list of more than a hundred molecules which can be used as a reference for the preparation of experiments developed for the Rosetta and Deep Space 4 cometary missions. We point out that further experiments are necessary to investigate the connections between the solid and gaseous phases of comets, especially studying the photodegradation of high molecular weight compounds which could be present in the nuclei.