The overwhelming majority of the astronomical objects are oxygen-rich, showing an abundance ratio C/O < 1 (by number). The so-called intrinsic carbon stars (C/O > 1) are formed during the AGB phase evolution of 1.5 ≤ M/M⊙≤ 3 stars through the mixing of fresh 12C from the interior of the star into the envelope during the 3rd dredge-up after each thermal pulse. They commonly show s-element enhancements produced by slow neutron captures provided by the 13C(α,n)16O reaction. The prototype of these stars are the AGB C-stars. Extrinsic carbon stars on the other hand, are formed in binary systems by mass transfer of carbon rich material from a former AGB star (now a white dwarf) onto the secondary star. Prototype of these class are the CH stars. A zoo of carbon-rich type stars exists, all being tracers of intermediate-age stellar populations. These stars are extremely useful for studies of the star formation history and chemical evolution of the galaxies. We present the detection and chemical analysis of carbon-enriched stars so far discovered within the Gaia-ESO survey. C-enriched candidates are identified from the analysis of a series of enhanced molecular features, measured through photometric and narrow-band spectroscopic filters. Then, the stellar parameters, C/O ratios and s-process element abundances are determined. The nature (intrinsic or extrinsic) of these carbon-enriched stars is discussed together with the expected impact of the Gaia mission on the knowledge of these objects in the Milky Way.