Cosmological numerical simulations predict that the SF in regular disk galaxies is feeding from metal-poor gas accreted from the cosmic web. The observational evidence for a relation between SFR and external gas accretion is both numerous and indirect (Sect. 3). One necessarily has to rely on modeling and analysis to identify the existing hints as actual signs of SF driven by metal-poor gas accretion. Thus, the comparison with numerical simulations and a meticulous interpretation of the observations turn out to be mandatory. There is no reason to believe that the magnitude of the problem will change significantly in the near future. The IGM gas is predicted to be tenuous and ionized, and so extremely elusive observationally. The IGM gas gets mixed with metal-rich outflows, and may loose its distinctive metal-poor character to complicate the study. In addition, metal-rich recycled material is also re-accreted, and often velocities are useless to separate inflows from outflows. Although things have much improved during the last few years, theoretical predictions are still very unspecific as far as the details is concerned. These details are needed to interpret particular observational results as evidence for accretion (Sect. 3.4). Finally, the difficulty to distinguish gas accretion events from gas-rich minor mergers confuses the interpretation even further (Sect. 3.3).
| Acronym | Expansion | Acronym | Expansion |
| ADS | NASA Astronomical Data System | M⁎ | Stellar mass |
| BCD | Blue compact dwarf | Mg | Gas mass |
| CGM | Circum-galactic medium | QBCD | Quiescent blue compact dwarf |
| DLA | Damped Lyman-α absorbers | QSO | Quasar |
| EAGLE | Evolution and Assembly of | SDSS | Sloan Digital Sky Survey |
| GaLaxies and their Environments | SF | Star formation | |
| Schaye et al. (2015) | SFR | Star formation rate | |
| FMR | Fundamental metallicity relation | SN, SNe | Supernova, Supernovae |
| HCM | HII-Chi-Mistry (Pérez-Montero 2014) | SPH | Smoothed particle hydrodynamics |
| IGM | Inter-galactic medium | UV | Ultraviolet |
| ISM | Interstellar medium | w | Mass loading factor (Eq. [4]) |
| IMF | Initial mass function | XMP | Extremely metal poor |
| MZR | (Stellar) Mass metallicity relation | Z | Metallicity of the gas (Eq. [9]) |
| MW | Milky Way | ||
Acknowledgements Special thanks are due to Casiana Munõz-Tuñón, Debra Elmegreen, and Bruce Elmegreen, for continuous support and for long thoughtful discussions on almost every topic included in the work. I am also indebted to Mercedes Filho, who pointed out many of the references cited in the work, and shared with me her expertise on H I. The interpretative aspects of the work own much to the collaboration with Claudio Dalla Vecchia and Daniel Ceverino. They were always willing discuss the physical aspects of the accretion and the star-formation process. Thanks are due to R. Amorín for the discussions that led to the writing of Sect. 3.7. Thanks are also due to the editors of the Book for giving me the opportunity to contribute, and for their patience to have my contribution finished. This work has been partly funded by the Spanish Ministry of Economy and Competitiveness, project Estallidos AYA2013–47742–C04–02–P.