In 1713, J. Bernoulli first discovered the method which one can produce those formulae for the sum $sumlimits_{iota=1}^{n};iota^k$ for any natural numbers k ([5],[6]). In this paper, we investigate for the historical background and motivation of the sums of powers of consecutive integers due to J. Bernoulli. Finally, we introduce and discuss for the subjects which are studying related to these areas in the recent.