The investigation of the magnetic characteristics of magnetic nanostructures (MNs) in various dimensions is a crucial direction of research in nanomagnetism, with MNs belonging to various dimensions exhibiting magnetic properties related to their geometry. A better understanding of these magnetic properties is required for MN manipulation. The primary tools for researching MNs are magnetic characterisation techniques with great spatial resolution and spin sensitivity. Micromagnetic simulation is another technique that minimises experimental costs, while providing information on the magnetic structure and magnetic behaviour, and has enormous potential for predicting, validating, and extending the magnetic characterisation results. This review first looks at the progress of research into quantitatively characterising the magnetic properties of low-dimensional (including 0D, 1D, and 2D) and 3D MNs in two directions: magnetic characterisation techniques and micromagnetic simulations, with a particular emphasis on the potential for future applications of these techniques. Single magnetic characterization techniques, single micromagnetic simulations, or a mix of both are utilised in these research studies to investigate MNs in a variety of dimensions. How the magnetic characterisation techniques and micromagnetic simulations can be better applied to MNs in various dimensions is then outlined. This discussion has significant application potential for low-dimensional and 3D MNs.