Emergent phenomena at complex-oxide interfaces have become a vibrant field of study in the past two decades due to the rich physics and a wide range of possibilities for creating new states of matter and novel functionalities for potential devices. Electronic-structural characterization of such phenomena presents a unique challenge due to the lack of direct yet non-destructive techniques for probing buried layers and interfaces with the required Angstrom-level resolution, as well as element and orbital specificity. In this review article, we survey several recent studies wherein soft x-ray standing-wave photoelectron spectroscopy, a relatively newly developed technique, is used to investigate buried oxide interfaces exhibiting emergent phenomena such as metal-insulator transition, interfacial ferromagnetism, and two-dimensional electron gas. Advantages, challenges, and future applications of this methodology are also discussed.