Negative ion sources for fusion are high densities plasma sources in large discharge volumes. There are many challenges in the modeling of these sources, due to numerical constraints associated with the high plasma density, to the coupling between plasma and neutral transport and chemistry, the presence of a magnetic filter, and the extraction of negative ions. In this paper we present recent results concerning these different aspects. Emphasis is put on the modeling approach and on the methods and approximations. The models are not fully predictive and not complete as would be engineering codes but they are used to identify the basic principles and to better understand the physics of the negative ion sources. e . (ii) A low electron temperature in the OPEN ACCESS RECEIVED