The China Space Station Telescope(CSST) is the next-generation Stage IV survey telescope. It can simultaneously perform multiband imaging and slitless spectroscopic wide-and deep-field surveys in ten years and an ultra-deep field(UDF) survey in two years, which are suitable for cosmological studies. Here we review several CSST cosmological probes, such as weak gravitational lensing, two-dimensional(2D) and three-dimensional(3D) galaxy clustering, galaxy cluster abundance, cosmic void, Type Ia supernovae(SNe Ia), and baryonic acoustic oscillations(BAO), and explore their capabilities and prospects in discovering new physics and opportunities in cosmology. We find that CSST will measure the matter distribution from small to large scales and the expansion history of the Universe with extremely high accuracy, which can provide percent-level stringent constraints on the property of dark energy and dark matter and precisely test the theories of gravity.