Asteroseismology is the study of stellar pulsations. Over the past decade, asteroseismology, in particular, the study of the solar-like oscillations, has entered its golden age and has caught attention across various fields, including exoplanet science and Galactic archaeology. With high-quality data from the CoRoT, Kepler, and TESS space missions, asteroseismology has been demonstrated to be an essential tool to characterise stars and probe stellar internal structure. In this thesis, I apply asteroseismic analyses to Kepler red giants showing a rich spectrum of solar-like oscillations, which are stochastically excited and intrinsically damped by surface turbulence. First of all, I give a brief introduction to some critical phases of stellar evolution and the fundamentals of asteroseismology. Then, I present in Chapter 2 the results on asteroseismology of 1523 red giants that were misclassified by the Kepler Input Catalog. A dedicated method was used to successfully discriminate for each star the real oscillation power excess from its alias. In Chapter 3, I present a catalog of global seismic parameters, masses, and radii for 16,000 red giants, which has been the largest and most homogeneous catalog. The results showed that oscillation amplitude and granulation power depend on mass and metallicity. Next, I show in Chapter 4 the results on asteroseismology of Long Period Variables (LPVs), which has provided strong evidence to address three long-standing open questions in LPVs. Oscillations and granulation are very valuable signals to characterise stars, but they introduce challenges to confirm and characterise small transiting exoplanets using radial velocity (RV) measurements. Chapter 5 shows predictions of RV jitter induced by oscillations and granulation for dwarfs and giants in terms of stellar parameters. The conclusions and some suggestions for future work are given in Chapter 6.