Retrieving concentrations of minor atmospheric trace gases from satellite observations is challenging due to their weak spectral signature. Here we present a new version of the ANNI (Artificial Neural Network for Infrared Atmospheric Sounding Interferometer, IASI) retrieval framework, which relies on a hyperspectral range index (HRI) for the quantification of the gas spectral signature and on an artificial feedforward neural network to convert the HRI into a gas total column. We detail the different steps of the retrieval method, especially where they differ from previous work, and apply the retrieval to three important volatile organic compounds: methanol (CH3OH), formic acid (HCOOH), and peroxyacetyl nitrate (PAN). The comparison of the retrieved columns with those from an optimal estimation inversion retrieval shows an overall excellent agreement: differences occur mainly when the sensitivity to the target gas is low and are consistent with the conceptual differences between the two approaches. We present retrieval examples over selected regions, comparison with previously developed products, and the global seasonal distributions including the first global distributions of PAN on a daily basis. The ANNI retrieval has been carried out on the whole time series of IASI observations (2007–2018), so that currently over 10 years of twice‐daily global CH3OH, HCOOH, and PAN total column distributions have been produced. This unique data set opens avenues for tackling important questions related to sources, transport, and transformation of volatile organic compounds in the global atmosphere.