The presently accepted "Theory of the Universe" was pioneered 60 years ago by Gamow, Alpher and Herman. As a consequence of the, later dubbed, Hot Big-Bang, matter was neutrons, and after some decay protons, and a history of successive captures built up the elements. It wasn't until some 15 years later (with the discovery of the Cosmic Microwave Background radiation) that Gamow and colleagues theories were validated and present day Standard Big-bang Nucleosynthesis theory was developed. We will discuss the importance of state of the art observations and modelling in the quest to determine precise values of the primordial abundance of D and 4He, using observations of astrophysical objects and modern day atomic parameters. In particular, we will present the search for understanding and coping with systematic errors in such determinations.