Hedgehogs in dimension one were introduced by Pérez-Marco in the '90s to study linearization properties and dynamics of holomorphic univalent germs of $(\mathbb{C}, 0)$ with a neutral fixed point. 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. This is based on joint work with T. Firsova, M. Lyubich, and R. Radu.