What can Euclid tell us about models beyond the concordance model?

Large scale structures and galaxy clusters are important and powerful natural laboratories to investigate effects of gravity and cosmic species, such as neutrinos. The best description that we have at the moment of the Universe as a whole is given by the concordance model, the LCDM model. Nevertheless, data at early and late times seem to be in conflict with each other and we do not know yet whether this is due to systematics or a first sign that we should move forward. The recently launched Euclid satellite is particularly suited to try giving such an answer and suggest whether the LCDM model is still the best description we have. In this talk I will present some recent results obtained within the Euclid collaboration which show how much better we will know our Universe but also the need of better theoretical and numerical tools to take advantage of information also at small scales.