The widely heralded and remarkable   progress in cosmology 
leading to  the emergence of a  'standard cosmological model’ has relied on  
certain key assumptions at various levels.  I review work along  
multiple facets, largely,  from the research program of  my group 
at IUCAA, that have all attempted to adopt  an agnostic approach in 
drawing cosmological inference independent  of such assumptions, 
in the context of  the exquisite   observations  of the Cosmic  Microwave 
Background CMB anisotropy by Planck. I dwell on the enigmatic 
Cosmic Hemispherical Anisotropy that continues to  challenge our 
understanding of the Universe.