In the current LIBOR transition to overnight–rate benchmarks, it is important to understand theoretically and empirically what distinguishes actual term rates from overnight benchmarks or “synthetic” term rates based on such benchmarks. The well–known “multi–curve” phenomenon of tenor basis spreads between term structures associated with different payment frequencies provides key information on this distinction. This information can be extracted using a modelling framework based on the concept of “roll–over risk”, i.e., the risk a borrower faces of not being able to refinance a loan at (or at a known spread to) a market benchmark rate. Separating the roll–over risk priced by tenor basis spreads into a credit–downgrade and a funding–liquidity component, the theoretical modelling and the empirical evidence show that proper term rates based on the new benchmarks remain elusive and that a multi–curve environment will persist even for rates secured by repurchase agreements.