abstract: In this talk we deal with a problem concerning minimal hypersurfaces in Carnot groups endowed with their Carnot- Caratheodory metric structure. We will study the Bernstein problem for entire regular intrinsic minimal graphs in the simplest Carnot group, i.e. the Heisenberg group $Hn$. In particular we will positively answer the Bernstein problem in the case $n = 1$ and we will provide counterexamples when $n \le 5$.