The transport of dust particles in tokamak fusion devices is studied using computer simulations with the dust transport code, DUSTT. Recent developments in modelling with the DUSTT code are reported. The improved model of dust dynamics in edge plasmas takes into account several additional effects, including thermionic and secondary electron emission which affects dust charging and heating, dust grain size effect on thermal radiation, and the presence of impurities in the plasma. It is shown that thermionic emission leads to enhanced dust heating by the plasma that boosts destruction of dust particles. The zone structure of tokamak plasmas is introduced for a qualitative analysis of dust survivability conditions. It is shown that a dust particle can experience net deposition in relatively cold carbon-contaminated plasma regions. Trajectories of sample dust particles in the DIII-D tokamak are simulated and analysed using the zone plasma description. Statistical averaging over an ensemble of particle trajectories is used to obtain spatial distributions of dust characteristics in the edge plasma of tokamaks. It is shown that transport of dust in tokamaks can significantly enhance penetration of carbon impurities towards the core plasma.