The idea of energy, matter, and motion has perplexed many philosophers and physicists from antiquity to modern physics, from Plato to Einstein. New and developing physical theories raise different interpretations of energy and matter but no complete theory of everything exists at present. However, there is a law we can almost take for granted - the Law of Conservation of Energy, it simply states that energy cannot be created nor destroyed although it can be transformed from one form to another. With an up-to-date history of the first law of thermodynamics, physicists in the field can have a sense of what has been done and what not. A complete overview of the rudimentary law would also provide a continuous timeline in which one can identify flaws in current theories. After establishing the foundational theory and history of conservation of energy, this literature review aims to provide a comparative study between the concept of mass and energy in two of the most profound physical theories - Quantum Mechanics and General Relativity. Subtle implication of numerous laws of thermodynamics and mass-energy equivalence like Dark Energy, Dark Matter, Higgs Mechanism and Blackhole Thermodynamics is studied in an introductory manner for potential history and correlate direct and indirect links to energy conservation.