Cosmology, the understanding of the evolution of entire Universe, has progressed very fast in the past several decades with the advances of modern telescopes. I will give a brief overview of the modern cosmology of the last century and highlight its phenomenal successes and distinctive challenges. I will explain how and why the measurements of cosmic microwave background radiation, the relics of the primordial elements, and the galaxy distribution on large scales can improve our understanding of the hot big bang. Then I will also discuss its distinctive challenges, present the observational frontiers for this (next) decade of cosmology, highlighting where the new physics may possibly emerge.