In this talk, we will explore properties of polynomials defined in Carnot groups, with a specific emphasis on their role in function approximation results. The first part of the talk will present a Lusin approximation theorem for real-valued functions in general Carnot groups. We will utilize a Lemma by De Giorgi, originally formulated in the Euclidean setting but recently extended to Carnot groups, to establish this result. This connection will serve as a bridge to the second part of the talk, where we will focus on Campanato spaces. These spaces of functions, through adjustments of their parameters, can characterize various other function spaces. The first part of the talk is based on collaborative work with A. Pinamonti and G. Speight, while the second part is an ongoing project with N. Cangiotti and A. Maione.