In the process known as quantum teleportation, quantum information encoded in a quantum particle, for example a photon, is transferred from one place to the other without ever moving the photon. Although quantum teleportation has been demonstrated with a variety of different systems, all have so far been limited in one crucial aspect: they only allow teleporting one degree of freedom. Here, Nai-Le Liu and colleagues demonstrate quantum teleportation of two degrees of freedom — spin and orbital angular momentum — in a single photon. Their experimental implementation is very complex and entails various innovative techniques, most notably a hybrid Bell-state measurement scheme. The intricacy of this scheme illustrates how difficult it will be to implement quantum teleportation of more complex quantum systems with more degrees of freedom. But this work represents a first and significant step in this direction.