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In this talk, we will introduce the interval optimization problems (IOPs) on Hadamard manifolds. To achieve the theoretical results, we build up some new concepts about gH-directional derivative, gH-Gateaux and gH-Frechet differentiability of interval valued functions and their properties on Hadamard manifolds. More specifically, we characterize the optimality conditions for the IOPs on the Hadamard manifolds. For unconstrained problems, the existence of efficient points and the steepest descent algorithm are investigated. To the contrast, the KKT conditions and exact penalty approach are explored in the ones involving inequality constraints. The obtained results pave a way to further study on Riemannian interval optimization problems (RIOPs).