Active Galactic Nuclei (AGN) are known to show flux variability over all observable timescales and across the entire electromagnetic spectrum. Over the past decade, a growing number of sources have been observed to show dramatic flux and spectral changes, both in the X-rays and in the optical/UV. Such events, commonly described as "changing-look AGN", can be divided into two well-defined classes. Changing-obscuration objects show strong variability of the line-of-sight column density, mostly associated with clouds or outflows eclipsing the central engine of the AGN. Changing-state AGN are instead objects in which the continuum emission and broad emission lines appear or disappear, and are typically triggered by strong changes in the accretion rate of the supermassive black hole. Here we review our current understanding of these two classes of changing-look AGN, and discuss open questions and future prospects.