Exploration of Altermagnetism in $\mathrm{RuO_{2}}$

The fundamental role of magnetic materials in modern science and technology has driven a rapid surge in research on unconventional magnetism in recent years. In particular, altermagnets, which simultaneously exhibit zero net magnetization in real space and anisotropic spin splitting in momentum space, have garnered significant interest for both fundamental physics and technological applications. Among these, $\mathrm{RuO_{2}}$ stands as the pioneering and most extensively studied altermagnet. While the intrinsic magnetic order of $\mathrm{RuO_{2}}$ is still a subject of active debate, numerous exotic phenomena characteristic of altermagnetism have been observed in $\mathrm{RuO_{2}}$ samples. In this review, we explore each facet of the altermagnetism through specific case studies in $\mathrm{RuO_{2}}$, systematically surveying its crystal and magnetic structures, electronic band properties, and transport phenomena. We critically assess the debate surrounding the intrinsic magnetism in $\mathrm{RuO_{2}}$, incorporating evidence from altermagnetic signatures in transport, as well as contrasting results from magnetic and spectroscopic measurements. Finally, possible future research directions in this field are discussed.