The remarkable success of recent cosmology in pinpointing a consistent concordance model relies on several foundational assumptions, including homogeneity, isotropy of the universe, and scale invariance, among others.  Increasingly precise cosmological observations, such as the exquisite measurements of the CMB sky from the
ESA Planck space mission, have opened up the possibility of robust, independent tests of these assumptions.
I will present key results from my research programs on this theme and review the current status of the research.