Absolutely Maximally Entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible partitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing and they provide the basis for novel tensor networks related to holography. We are going to define them, show ways to build them in different Hilbert spaces, talk about their applications and show their mathematical relations with combinatorial designs and multiunitarity.