Associated with every positive interest term structure there is a probability density function over the positive half-line. This fact can be used to turn the problem of term structure analysis into a problem in the comparison of probability distributions, an area well developed in statistics, known as information geometry. The information-theoretic and geometric aspects of term structures thus arising are here illustrated. In particular, we introduce a new term structure calibration methodology based on maximization of entropy, and also present some new families of interest rate models arising naturally in this context.