I will describe the exciting prospects for advances in cosmology with the advent of the Square Kilometre Array (SKA), which will open a new window on the cosmos and cover larger cosmic volumes than ever before. The combination of optical surveys like Euclid and the Rubin Observatory (LSST) with the SKA promises to provide excellent precision in measuring Dark Energy and Dark Matter. But in addition, SKA surveys will deliver a new capacity to make tests of the foundations of our model of the Universe. In particular, I will discuss probing the primordial Universe via fossil signals in the galaxy distribution, and testing the Cosmological Principle via radio galaxies.