Information geometry involves the use of differential geometric tools to describe the manifold of probability density functions, and allows one to investigate the intrinsic properties of statistical models as opposed to their parametric representations. In particular, we will discuss how divergence functions, and their induced geometric structures, like the Riemannian metric, dually flat affine connections, and curvature relate to statistical issues like asymptotic efficiency of maximum likelihood estimators as well as optimization algorithms on the manifold of probability distributions.