Neutrino oscillation experiments have shown neutrinos to be massive, therefore they affect the evolution of structures of the Universe at the linear and non-linear levels. First, I will discuss how to model the non-linear matter power spectrum in a massive neutrino cosmology, using an extended version of the halo model. I will show the comparison between these theoretical predictions and the results from N-body simulations. Second, since cosmic voids are expected to be good environments to characterise the neutrino-induced effect on the matter distribution, I will present the results of a numerical study of void properties that aims to identify these effects. Finally, I will discuss a model for describing the shape and evolution of void density profiles.