The LIBOR Market Model, developed by Brace and Musiela, adapts the Heath-Jarrow-Morton framework to handle market quoted rates like LIBOR rates. They use a parameterization method to model interest rate dynamics and choose volatility functions to ensure lognormal behavior for LIBOR rates. The model is also used to price interest rate caps and swaptions. Additionally, the model can price interest rate caplets accurately even when the forward rate dynamics are Gaussian.