  We provide a unified framework for modeling LIBOR rates using general
semimartingales as driving processes and generic functional forms to describe
the evolution of the dynamics. We derive sufficient conditions for the model to
be arbitrage-free which are easily verifiable, and for the LIBOR rates to be
true martingales under the respective forward measures. We discuss when the
conditions are also necessary and comment on further desirable properties such
as those leading to analytical tractability and positivity of rates. This
framework allows to consider several popular models in the literature, such as
LIBOR market models driven by Brownian motion or jump processes, the L\'evy
forward price model as well as the affine LIBOR model, under one umbrella.
Moreover, we derive structural results about LIBOR models and show, in
particular, that only models where the forward price is an exponentially affine
function of the driving process preserve their structure under different
forward measures.
