For centuries, magnetism of materials has been an inevitable part of human civilization. Only in the last century, the mysteries of magnetism started to unfold thanks to the development of quantum theory of solids. Nevertheless, even today, new exotic phenomena related to magnetism keep on surprising us and provide an enormous playground for theoreticians and experimentalists to unravel the complexities. In this thesis, the magnetic properties of materials are studied from different aspects by using first-principle density functional theory. Specifically, we investigated the substituted quadruple perovskite compounds ACu₂Fe₂Re₂O₁₂ (A=Ca, Sr, Ba, Pb, Sc, Y, La). Seven different A-site doped structures are studied, including divalent and trivalent charge substitutions. We found that all these compounds are half-metallic ferrimagnets with large magnetization and high transition temperatures (above 405K). Interestingly, the trivalent atom doping at the A-site can significantly increase the transition temperature. The exchange mechanism is explained by the super-exchange in the Re-Cu and Re-Fe pairs. Moreover, we investigated three different two-dimensional magnets, CrI₃, FeS₂, and CrO. For the first project, we studied stacking dependent magnetic properties of CrI₃. It was found that the magnetic ground state can be tuned by the stacking sequences. In the second project, we studied the monolayer FeS₂. The results show that the structures with FM and AFM configuration are close in energy. By performing further spin-spiral calculations, we found that the ground state magnetic configurations are different with different crystal structures. This structure dependent magnetic property indicates the existence of spin-lattice coupling in this material. In the third project, we predicted a monolayer CrO, which is a Weyl semimetal with antiferromagnetism up to room temperature. Finally, a heterostructure structure with G-type SrMnO₃ supported on SrTiO₃ substrate is investigated. We found that with a 2.9% tensile strain introduced by the substrate, the SrMnO₃ keeps as G-type AFM. Moreover, oxygen vacancy intends to stay at the surface. Interestingly, this vacancy induces the AFM-FM transition on the specific layer due to the double exchange mechanism.