A collection of works stretching from low- to three-dimensional magnetism are presented, studied mostly through muon spin rotation, relaxation and resonance (µ +SR). The theoretical background of this technique is outlined in Chapter 2, which introduces the subject from the muon particle as an astro[1]nomical particle to how they are produced here on Earth. Given the specific properties of weak particle interactions, previous generations of scientists developed the technique of µ +SR. Special care is taken to explain how the anti-muon interacts with magnetic fields and the resulting behaviour of the anti-muon in a given magnetic field configuration. The fundamental principle of µ +SR is to interpret the resulting muon behaviour in order to unveil microscopic details of the compounds of interest. Other experimental techniques were utilised to confirm the assessment made by µ +SR and to probe different aspects of the compounds being studied. Specifically, neutron and X-ray scattering were performed; the corresponding theoretical background is presented in Chapter 4. Interpretations, conclusions and discussions regarding the studied compounds are presented in Chapter 5. This chapter is divided into four parts depending on the study: one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) magnets and studies related to µ +SR in general. The 1D compounds comprise mostly samples within the Hollandite family, which exhibit quasi-1D chains of transition metal ions. These chains may in certain cases facilitate interactions in a 1D fashion, which is a very interesting feature. In particular, a quantum spin liquid phase is found in one of the compounds, stabilised by a peculiar form of charge ordering occurring at high temperature. Microscopic evidence for the absence of a Peierls transition in a ferromagnetic metal-insulator transition compound is presented as well. The 2D compounds include layer-structured samples in which intralayer interactions are assumed to be dominant. Interestingly, the ground state was found to not be governed only by the intralayer interactions, at least in one of the compounds. Instead, the charge distribution in between the layers seems to have a role to play, as the specific cation ordering determined the ground state. A study in which this distribution is changed to study its effect on the ground state is presented. The 3D magnets considered here exhibit unique interactions available in these compounds. Complicated phases emerge above the transition temperature due to modulation of interactions in space. Finally, a collection of interesting studies related to general µ +SR are included in Chapter 5. These include a study of lithium ion diffusion anisotropy detected for the first time by µ +SR and a semantical discussion related to the term muonium. Other studies not related to this thesis are listed in Articles not included in this thesis. This thesis concludes with Chapter 6, which briefly summarises the work and the resulting outcomes. Most importantly, a smaller discussion on the future of physics is presented, considering its implications for society and science as a whole.