The nature of the Cooper pairing in the paradigmatic unconventional superconductor Sr2RuO4 is an outstanding puzzle in condensed matter physics.Despite the tremendous efforts made in the past twenty-seven years,neither the pairing symmetry nor the underlying pairing mechanism in this material has been understood with clear consensus.This is largely due to the lack of a superconducting order that is capable of interpreting in a coherent manner the numerous essential experimental observations.At this stage,it may be desirable to reexamine our existing theoretical descriptions of superconducting Sr2RuO4.This review focuses on several recent developments that may provide some clues for future study.We highlight three separate aspects:1)any pairing in the Eu symmetry channel,with which the widely discussed chiral p-wave is associated,shall acquire a 3D structure due to spin-orbit entanglement;2)if the reported Kerr effect is a superconductivity-induced intrinsic bulk response,the superconductivity must either exhibit a chiral character,or be complex mixtures of certain set of helical p-wave pairings;3)when expressed in a multiorbital basis,the Cooper pairing could acquire numerous exotic forms that are inaccessible in single-orbital descriptions.The implications of each of these new perspectives are briefly discussed in connection with selected experimental phenomena.