Iridates have been providing a fertile ground for studying emergent phases of matter that arise from delicate interplay of various fundamental interactions with approximate energy scale. Among these highly focused quantum materials, perovskite Sr2IrO4 belonging to the Ruddlesden-Popper series stands out and has been intensively addressed in the last decade, since it hosts a novel Jeff = 1/2 state which is a profound manifestation of strong spin-orbit coupling. Moreover, the Jeff = 1/2 state represents a rare example of iridates that has been better understood both theoretically and experimentally. In this progress report, we take Sr2IrO4 as an example to overview the recent advances of the Jeff = 1/2 state in two aspects: materials fundamentals and functionality potentials. In the fundamentals part, we first illustrate basic issues for the layered canted antiferromagnetic order of the Jeff = 1/2 magnetic moments in Sr2IrO4, and then review the progress of the antiferromagnetic order modulation through diverse routes. Subsequently, for the functionality potentials, fascinating properties such as atomic-scale giant magnetoresistance, anisotropic magnetoresistance, and nonvolatile memory, will be addressed. This report will be concluded with our prospected remarks and outlooks.