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We examine the role of information geometry in the context of classicalCram\'er-Rao (CR) type inequalities. In particular, we focus on Eguchi's theoryof obtaining dualistic geometric structures from a divergence function and thenapplying Amari-Nagoaka's theory to obtain a CR type inequality. The classicaldeterministic CR inequality is derived from Kullback-Leibler (KL)-divergence.We show that this framework could be generalized to other CR type inequalitiesthrough four examples: $\alpha$-version of CR inequality, generalized CRinequality, Bayesian CR inequality, and Bayesian $\alpha$-CR inequality. Theseare obtained from, respectively, $I_\alpha$-divergence (or relative$\alpha$-entropy), generalized Csisz\'ar divergence, Bayesian KL divergence,and Bayesian $I_\alpha$-divergence.

Information Geometry and Classical Cram\'{e}r-Rao Type Inequalities