Stars, as the fundamental constituents of the Universe, shape its chemical evolution and pro- vide essential insights into the building blocks of life. Recent advancements in stellar characteriza- tion, facilitated by space-based photometry missions like CoRoT, Kepler, and TESS, have propelled asteroseismology to unprecedented heights. By studying stellar oscillations, analogous to Earth’s seismology, we gain access to the internal layers of distant stars, enabling us to constrain trans- port processes and refine stellar parameters such as mass, radius, and age. Precise and accurate stellar models are pivotal in understanding the evolution of planetary systems and unraveling the galactic history through Galactic Archeology. Looking ahead, the success of past missions sets the stage for future missions such as PLATO and CubeSpec, wherein asteroseismic modelling will play a key role. Additionally, large-scale surveys such as GAIA, GALAH, and APOGEE contribute a wealth of complementary data, ushering in a new golden era of data-driven stellar physics.

In this thesis we aim to improve the asteroseismic characterisation of solar-like stars using for- ward and inverse techniques. The first part of the manuscript reviews the historical, observational, and theoretical foundations of asteroseismic modelling, providing a comprehensive framework for our research efforts. We then explore two key areas of study. Firstly, our investigation focuses on the refinement of the modelling strategy and associated tools, involving a detailed examina- tion of the theoretical advancements we have undertaken. This includes a detailed discussion of the applications of these developments to observed stellar targets. Secondly, we direct our fo- cus towards the physical ingredients employed in stellar models, and conduct an exploration of optimisation possibilities in this regard. Notably, we present the results of our studies aimed at probing the properties of convective cores and constraining the transport of angular momentum in main-sequence solar-like stars. The concluding part of the manuscript synthesises the results of our thesis. Additionally, we also engage in a discussion of future perspectives, shedding light on potential avenues for further research and advancement.