Submanifolds with intrinsic Lipschitz regularity in Carnot groups (i.e.,stratified groups endowed with a sub-Riemannian structure) can beintroduced using the theory of intrinsic Lipschitz graphs started yearsago by B. Franchi, R. Serapioni and F. Serra Cassano. One of the mainrelated questions concerns a Rademacher-type theorem about the almosteverywhere existence of a tangent plane to intrinsic Lipschitz graphs:after a gentle introduction to the topic, I will discuss a positivesolution to the problem in Heisenberg groups. The proof uses thelanguage of currents in Heisenberg groups (in particular, a version ofthe Constancy Theorem) and a number of complementary results such asextension and smooth approximation theorems for intrinsic Lipschitzgraphs. I will also show a recent example, joint with A. Julia and S.Nicolussi Golo, of an intrinsic Lipschitz graph in a Carnot group thatis nowhere intrinsically differentiable. The talk will be kept at anintroductory level.