If the domain space and the range space are the same Euclidean space with dimension greater than 1, the Aleksandrov problem has already been solved by the Beckman–Quarles theorem. W. Benz and H. Berens also solved the extended Aleksandrov problem under the additional conditions that the domain is a real normed space with dimension greater than 1, the range is a strictly convex real normed space, two distances are preserved, and that the ratio of the two distances is an integer. In this chapter, we investigate the Aleksandrov–Rassias problems, which focus on cases where the domain and range of the mapping involved differ, and cases where the ratio of two distances that are preserved is not an integer. By introducing interesting examples and counterexamples related to these topics, we try to help readers easily grasp the core reality of the problem.