In this talk I will provide a comprehensive introduction to the field of stellar oscillations by focusing on stars of low- and intermediate-mass from the main sequence up to the core-Helium-burning phase of the stellar evolution. I will show how asteroseismology can be used not only to understand stars and their evolution in detail, but to also probe star cluster formation and the structure and evolution of our Galaxy. This will comprise some recent highlights of my research, which are related to the study of stellar spin orientation and of stellar granulation. Finally, I will discuss the present and future challenges in analyzing asteroseismic data delivered by space missions such as NASA Kepler, TESS, and soon ESA PLATO, and how my research is trying to overcome these challenges through the development of novel techniques based on Bayesian approaches.