The paper discusses the combined effects of electron correlation and spin-orbit coupling in heavy transition metal compounds with 4d and 5d elements, focusing on emergent quantum phases and transitions. The authors highlight the influence of spin-orbital entanglement, which can significantly alter electronic and magnetic structures. In the weak-to-intermediate correlation regime, non-trivial band topology leads to various phases such as topological insulators, Weyl semi-metals, axion insulators, and topological Mott insulators. The paper uses pyrochlore iridates as a primary example to illustrate these phenomena. In the strong correlation regime, spin-orbital entanglement fully or partially removes orbital degeneracy, reducing or avoiding the Jahn-Teller effect. This leads to enhanced quantum fluctuations and the potential for exotic quantum ground states, such as quantum spin liquids and multi-polar ordered phases. The authors also discuss the experimental status and future directions for these materials.The paper discusses the combined effects of electron correlation and spin-orbit coupling in heavy transition metal compounds with 4d and 5d elements, focusing on emergent quantum phases and transitions. The authors highlight the influence of spin-orbital entanglement, which can significantly alter electronic and magnetic structures. In the weak-to-intermediate correlation regime, non-trivial band topology leads to various phases such as topological insulators, Weyl semi-metals, axion insulators, and topological Mott insulators. The paper uses pyrochlore iridates as a primary example to illustrate these phenomena. In the strong correlation regime, spin-orbital entanglement fully or partially removes orbital degeneracy, reducing or avoiding the Jahn-Teller effect. This leads to enhanced quantum fluctuations and the potential for exotic quantum ground states, such as quantum spin liquids and multi-polar ordered phases. The authors also discuss the experimental status and future directions for these materials.