We examine the role of information geometry in the context of classical Cram{\'{e}}r–Rao (CR) type inequalities. In particular, we focus on Eguchi's theory of obtaining dualistic geometric structures from a divergence function and then applying Amari–Nagoaka's theory to obtain a CR type inequality. The classical deterministic CR inequality is derived from Kullback–Leibler (KL) divergence. We show that this framework could be generalized to other CR type inequalities through four examples: $\alpha$-version of CR inequality, generalized CR inequality, Bayesian CR inequality and Bayesian $\alpha$-CR inequality. These are obtained from, respectively, I$\alpha$-divergence (or relative $\alpha$-entropy), generalized Csisz{\'{a}}r divergence, Bayesian KL divergence and Bayesian I$\alpha$-divergence.