  The correspondence principle between strings and black holes is a general
framework for matching black holes and massive states of fundamental strings at
a point where their physical properties (such as mass, entropy and temperature)
smoothly agree with each other. This correspondence becomes puzzling when
attempting to include rotation: At large enough spins, there exist degenerate
string states that seemingly cannot be matched to any black hole. Conversely,
there exist black holes with arbitrarily large spins that cannot correspond to
any single-string state. We discuss in detail the properties of both types of
objects and find that a correspondence that resolves the puzzles is possible by
adding dynamical features and non-stationary configurations to the picture. Our
scheme incorporates all black hole and string phases as part of the
correspondence, save for one outlier which remains enigmatic: the near-extremal
Kerr black hole. Along the way, we elaborate on general aspects of the
correspondence that have not been emphasized before.
