What Tc tells

•Highly oxidized cuprates are promising for high Tc.•Non-equilibrium phases obtained at interfaces and by quenching represent a huge phase space with opportunities for new discoveries.•Negative U pairing centers could lead to high Tc.•USOs, of which we have given a few promising examples, require further investigation.•Searching for new and enhanced Tc’s Tc’s remains a promising and fertile frontier.

Superconductivity has continued to be a fascinating phenomenon ever since its discovery in 1911. The magnitude of the transition temperature, Tc, provides valuable insight into the underlying physics. Here we provide select examples of the extensive research that has been done towards understanding Tc, and some cases where further investigation is called for. We believe that searching for new and enhanced Tc’s remains a fertile frontier.