The chapter discusses the “great controversy” of modern cosmology. The controversy began after World War II and lasted for a couple of decades. In the controversy, the proponents of various iterations of the steady-state theory of the universe collided with the pioneers of the emerging big-bang expanding universe theory. The latter theory triumphed, while establishing empirical standards of cosmological theories and breaking the stigma of cosmology as an unscientific subject that lurked in the science community. Parsimonious observational criteria were devised for the key cosmological parameters, including the age of the universe, source counts, redshift–magnitude relation, and redshift–angular size relationship. The chapter also discusses how the relation between redshift in the spectrum and magnitude was pioneered by Hubble and slowly perfected by tests on different celestial objects, from galaxies to Type Ia supernova stars.