  Twenty-five years after the invention of quantum teleportation, the concept
of entanglement gained enormous popularity. This is especially nice to those
who remember that entanglement was not even taught at universities until the
1990's. Today, entanglement is often presented as a resource, the resource of
quantum information science and technology. However, entanglement is exploited
twice in quantum teleportation. First, entanglement is the `quantum
teleportation channel', i.e. entanglement between distant systems. Second,
entanglement appears in the eigenvectors of the joint measurement that Alice,
the sender, has to perform jointly on the quantum state to be teleported and
her half of the `quantum teleportation channel', i.e. entanglement enabling
entirely new kinds of quantum measurements. I emphasize how poorely this second
kind of entanglement is understood. In particular, I use quantum networks in
which each party connected to several nodes performs a joint measurement to
illustrate that the quantumness of such joint measurements remains elusive,
escaping today's available tools to detect and quantify it.
