The "Dark Energy and Massive Neutrino Universe" project is a set of 14 large N-body simulations to study the evolution of large scale structures in the presence of massive neutrinos and dynamical dark-energy, parametrised according to Chevallier, Polarski & Linder. As shown in recent studies, the effect of the neutrino mass on the large scale structure of the Universe (growth rate and BAO) cannot be completely disentangled from that of a dynamical dark energy, undermining the interpretation of cosmological observations. Non-linear modelling of structure formation is therefore needed to fully exploit the current and future very large cosmological datasets. These simulations are the first in the literature to simultaneously deal with massive neutrinos and different dark-energy equations of state. The simulations are characterised by a box side L=2 Gpc/h, a particle number of N=2x(2048)^3 (the factor of 2 stands for CDM and neutrino particles), and a mass resolution for CDM particles of about 8x10^10 M_sun/h. Given their large volume and good mass resolution, the DEMN-Universe simulations will be used to generate mock galaxy/void catalogs and CMB/weak-lensing/SZ/ISW/Rees-Sciama maps. This will help to predict with how much accuracy the combination of future cosmological probes will be able to constrain the neutrino mass in the presence of an evolving dark energy, and viceversa. I will present recent results from the DEMN-Universe suite, together with possible applications to Euclid.