A review on quantum teleportation, a primitive in many protocols in quantum information science, is published in Nature Photonics. Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive in a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we review the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms, and solid-state systems. Analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations. This article has been written together with the friends and colleagues Stefano Pirandola, Christian Weedbrook, Akira Furusawa, and Samuel L. Braunstein from York, Toronto, and Tokyo.