After introducing the standard model of cosmology and its fundamental pillars, I will discuss its successes and problems. Based on these I will analyze the fundamental assumptions of the underlying model and how one can consistently try to extend/generalize them. I will then discuss how we can use cosmological and astrophysical observations to test gravity and our fundamental assumptions, with a special emphasis on gravitational waves measurements and the future ahead. Anybody unable to attend the colloquium in person is invited to participate by Zoom through the link: https://zoom.us/j/94202622849?pwd=dGlPQXBiUytzY1M2UE5oUDRhbzNOZz09 (Meeting ID: 942 0262 2849 Passcode: 792771)