I will briefly discuss the current status of standard model of cosmology
with the emphasis on the GR as its main building block.
Then will stress out why is it so important to obtain
new and independent tests of Einstein’s gravity on cosmological scales.
I shall discuss some of the currently considered and available tests
of the theory and will conclude by presenting my work towards constituting
new and largely model-independent tests of GR on intergalactic
and cosmological scales.