In this talk we are going to present some recent Lipschitz regularity results for functionals and systems with non standard growth, without further structure conditions on the integrand, both in the scalar and in the vector case. This is a joint project with Paolo Marcellini and Elvira Mascolo. In the last part of the talk, we will complement these results by dealing with obstacle problems. This is a joint project with Antonia Passarelli di Napoli and Michele Caselli.