This review describes recent significant research developments made on the layered perovskite Sr₂RuO₄ and discusses current issues from both experimental and theoretical perspectives. Since the discovery of superconductivity in Sr₂RuO₄ in 1994, studies using high-quality single crystals quickly revealed it to be an archetypal unconventional superconductor among strongly correlated electron systems. In particular, it was thought that the spin-triplet chiral p-wave superconducting state, which breaks time-reversal symmetry, was a prominent possibility. In 2019, however, a new development overturned the past experimental results, and spin-singlet-like behavior became conclusive. Furthermore, innovation in uniaxial strain devices has stimulated researchers to explore changes in the superconducting state by controlling the symmetry and dimensionality of the Fermi surfaces and enhancing the superconducting transition temperature T_c from 1.5 to 3.5 K. A spin-singlet chiral d-wave superconducting state is consistent with most of these recent experimental results. Nevertheless, there are still unnatural aspects that remain to be explained. The focus of this review is on unraveling this mystery. Unlike many other unconventional superconductors, the normal state of Sr₂RuO₄ exhibits typical Fermi liquid behavior. Nevertheless, to elucidate its superconducting state, it may be essential to go beyond the traditional framework of unconventional superconductivity and recast the theory explicitly considering the multi-orbital aspects of its electronic states. In this review, we describe the frontiers of superconductivity research in Sr₂RuO₄ and discuss how the remaining issues may be resolved.