A body of experimental evidence showing that Sr₂RuO₄ is spin-triplet, p-wave superconductor, an electronic analog of superfluid ³He as predicted theoretically, has been accumulating over the years. In particular, the Josephson coupling and phase-sensitive measurements on the pairing symmetry in Sr₂RuO₄ carried out at Penn State demonstrated clearly that Sr₂RuO₄ is an odd-parity superconductor with the d-vector along the caxis. Combining with the group theory analysis, these findings also suggested that Sr₂RuO₄ should possess the very special p±ip pairing state, making Sr₂RuO₄ a topological superconductor featuring Majorano zero energy modes. On the other hand, whether Sr₂RuO₄ is such a chiral p-wave superconductor has not been settled thus far because of the lack of direct experimental evidence for chiral edge currents that must be present in order for Sr₂RuO₄ to be chiral. In this talk, I will discuss the current status of the Sr₂RuO₄research and our most recent efforts in detecting the chiral edge currents. I will also discuss our future research in Sr₂RuO₄ and 2D crystals of single- and multi-layer transition metal chalcogendes in which unconventional superconductivity is also expected.