This chapter depicts the evolution of a modern area of mathematics namely ‘fixed point theory’. Description of the theory right from its potential origin in seventeenth century to 1950 is attempted. The theorems which made a significant impact on the development are mentioned with the outline of their proofs. Gradual progression of the fixed point theorems in terms of incremental changes in contraction conditions and in terms of various spaces is mentioned. The contribution of this novel branch of mathematics in applications in science and engineering is also highlighted.