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Many late-type stars across the Milky Way exhibit observable pulsations similar to our Sun that open up a window into stellar interiors. The NASA Kepler mission, a space-based photometric telescope, measured the micro-magnitude luminosity fluctuations caused by solar-like oscillations of tens of thousands of stars for almost 10 years. Detailed stellar structure, evolution, and oscillation theoretical work established in the decades before, such as predictions about mode mixing in the interior of red-giant stars, among many others, now had voluminous precision data against which it could be tested. The overwhelming result is the general validation of the theory of stellar oscillations as well as stellar-structure models; however, important gaps in our understanding of interior physics was also revealed by Kepler. For example, interior rotation, convection, and mixing processes are complex phenomena not fully captured by standard models. This review explores some of the important impacts Kepler observations of solar-like oscillations across the cool end of the H-R diagram has had on stellar astrophysics through the use of asteroseismology.

The scaling relations for solar-like oscillations provide a translation of the features of the stochastic low-degree modes of oscillation in the Sun to predict the features of solar-like oscillations in other stars with convective outer layers. This prediction is based on their stellar mass, radius, and effective temperature. Over time, the original scaling relations have been reversed in their use from predicting features of solar-like oscillations to deriving stellar parameters. Updates to the scaling relations as well as their reference values have been proposed to accommodate for the different requirements set by the change in their use. In this review the suggestions for improving the accuracy of the estimates of stellar parameters through the scaling relations for solar-like oscillations are presented together with a discussion of pros and cons of different approaches.