The question of how Newton came to develop the principles of mechanics has intrigued historians of science and a few physicists for a long time. In the early part of the 17-th century, Kepler announced three empirical laws for planetary motion, which he discovered by fitting very accurate astronomical observations of Mars obtained by Tycho Brahe. Then the problem of finding the physical origin for these laws became a fundamental task for astronomers and natural philosophers. A complete solution to this problem, however, was not obtained until Newton formulated his famous laws of motion, and developed the necessary mathematical methods including the calculus to solve a vast array of problems in astronomy and physics, which he published in the Principia in 1687. In the past, detailed accounts have been given for the path that led Newton to his discoveries, but some crucial steps have been left out or misunderstood, particularly in regard to the seminal role of Robert Hooke, whose 1679 correspondence with Newton broke an impasse in Newton's work. In this talk I will clarify these historical steps, and discuss Newton's perturbations methods, attributed later to Euler and Lagrange, to treat the notoriously difficult three- body problem which have kept mathematicians occupied up to the present time.