Comets are some of the most pristine bodies of the solar system. As such, cometary ices retain invaluable clues about the evolution of volatile material within the proto-planetary nebula. Understanding the composition of comets and its diversity is of great interest to decipher scenarios of early solar system evolution. Following the latest ground-based observations and the very successful ROSETTA mission, tens of primary volatiles have now been detected in the coma of comets. Isotopic ratio measurements (of H, C, N, and O for example) have provided insights to enrichment and fractionation mechanisms at play in the primitive solar nebula. Besides, large optical photometric and spectroscopic databases containing more than 100 objects have allowed to perform taxonomic classifications of comets based on the abundance ratios of fragment species, and efforts have been made to search for links between those classifications and the formation environment of comets in the proto-planetary disk. Similarly, taxonomies are now starting to arise from the abundance ratios of primary volatiles measured in more than thirty comets at infrared or radio wavelengths. This talk will summarise the current understanding of comet composition and emerging taxonomies.