New advances in nebular photoionisation modelling
  The study of photoionised gas in planetary nebulae (PNe) has played a major role achieving, over the years, a better understanding of a number of physical processes pertinent to a broader range of fields than just PNe studies, ranging from atomic physics to stellar evolution. Whilst empirical techniques are routinely employed for the analysis of the emission line spectra of such objects, the accurate interpretation of the observational data often requires the solution of the radiative transfer (RT) problem in the nebula, via the application of a photoionisation code.The development of the codes has been driven by the observational constraints available, but also compromised by the available computer power. Modern codes are faster and more flexible, with the ultimate goal being the achievement of a description of the observations relying on the smallest number of parameters possible. In this light, recent developments have been focused on the inclusion of new atomic data, the inclusion of a realistic treatment for dust grains mixed in the ionised and photon dominated regions (PDRs) and the expansion of some codes to PDRs with the inclusion of chemical reaction networks. Furthermore the last few years have seen the development of fully 3D photoionisation codes based on the Monte Carlo method. A review of the photoionisation codes currently in use is given here, with emphasis on recent developments, including the expansion of the models to the 3D domain, the identification of new observational constraints and how these can be used to extract useful information from realistic models.[Abridged] 
Barbara Ercolano