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Partition Analysis was introduced by MacMahon in the beginning of 20th century, as a method to attack problems of integer partitions subject to linear Diophantine constraints. His method did not become mainstream among mathematicians and was forgotten for half a century. In the turn of last century Andrews, Paule and Riese gave fully algorithmic versions of Partition Analysis and some years later Xin came up with an improved algorithmic method. Recently, in joint work with Breuer we gave a version of Partition Analysis based on polyhedral geometry. In this talk, we will review the history of Partition Analysis from its inception to date, mostly looking at it from a geometric perspective and exploring the analytic aspects of early methods in contrast to the formal nature of the more recent ones.