Teleportation of physical objects, transferring from one place to another without passing through intermediate locations, is not possible. However, teleportation of quantum states (the full information of quantum objects) is possible. Quantum teleportation is the faithful transfer of quantum states between systems, relying on the prior establishment of entanglement and using only classical communication during the transmission. In this talk I will first give an introduction of quantum teleportation and then present our on?going free?space quantum teleportation experiment between the two Canary Islands La Palma and Tenerife, separated by 144 km. Our scheme combines a Bell?state measurement, capable to identify two of the four Bell?states, with an actively triggered unitary transformation depending on its outcome. The scheme achieves the optimal teleportation efficiency achievable with linear optical elements. Our work is essential for showing the feasibility of satellite?based experiments and is an important step towards quantum?communication applications on a global scale.