Hedgehogs in dimension one were introduced by Pérez-Marco in the '90s in order to study linearization properties and dynamics of holomorphic univalent germs of $(\mathbb{C},0)$ with a neutral fixed point at the origin. In this talk we discuss hedgehogs and their dynamics for germs of holomorphic diffeomorphisms of $(\mathbb{C}^n,0)$ with a fixed point at the origin with exactly one neutral eigenvalue. We will also survey the results of Pérez-Marco and show how to transport them to higher dimensions. This is based on joint work with T. Firsova, M. Lyubich, and R. Radu.