This talk will focus on the version of de Rham's theory adapted to the setting of derived manifolds and derived differentiable stacks. In particular, we will discuss two (secretly three) different notions of de Rham stacks and associated "cohomology theories". We will see how they differ and how one can understand the de Rham theorem and Riemann--Hilbert correspondence in classical differential topology by comparing them. Time permitting, I will also say a few words about how these results fit into the broader context of derived analytic geometry.