Power system oscillation damping remains as one of the major concerns for secure and reliable operation of large power systems, and is of great current interest to both industry and academia. The principal reason for this is that the inception of poorly-damped low-frequency inter-area oscillations (LFIOs) when power systems are operating under stringent conditions may lead to systemwide breakups or considerably reduce the power transfers over critical corridors. With the availability of high-sampling rate phasor measurement units (PMUs), there is an increasing interest for effectively exploiting conventional damping control devices, such as power system stabilizers (PSSs), by using these measurements as control input signals. In this paper, we provide a comprehensive overview of distinct elements (or "building blocks") necessary for wide-area power system damping using synchrophasors and PSSs. These building blocks together shape a tentative methodical framework, and are disposed as follows: (1) fundamental understanding of the main characteristics of inter-area oscillations, (2) wide-area measurement and control systems (WAMS and WACS) and wide-area damping control (WADC), (3) advanced signal processing techniques for mode property identification, (4) methods for model-based small-signal analysis, (5) control input signals selection, and (6) methods for PSS control design. We also describe the latest developments in the implementation of synchrophasor measurements in WAMS and WACS as well as their prospectives for WADC applications. This paper serves both to abridge the state-of-the-art in each of these elements, and to accentuate aspiring ideas in each building block.