The history of the science of meteorology, recognized as a multi-disciplinary field of physical sciences, can be classified into several periods depending on the scope and the required details of the undertaken study. In this paper, the evolution of the science of meteorology has been presented through the most significant milestones within each classified period. Diachronically, the evolution is divided into three major periods. The first period is called the 'hypothesis period', and covers a period from the first attempts of man to address weather phenomena up to ca. 1600 AD. The second period, called the 'instrumental period', from ca. 1600 AD up to approximately 1800 AD, is characterized by the invention of the basic instruments used in weather observations. Finally, the third period from ca. 1800 AD till today, called the 'scientific period', covers scientific and technological advances. Within each period, the corresponding milestones are identified and presented accordingly.