The subjects of this paper are a discussion of the methodology of relative age determination by impact crater statistics, a comparison of currently proposed Martian impact chronologies for the determination of absolute ages from crater frequencies, a report on our work of dating Martian volcanoes and erosional features by impact crater statistics, and an attempt to understand the main features of Martian history through a synthesis of our crater frequency data and those published by other authors. Two cratering chronology models are presented and used for inference of absolute ages from crater frequency data: model 1, with nearly equal Martian and lunar cratering rates around (ca.) 4- to 10-km crater sizes, and model II. equivalent to model I for ages >3.5 ⋅ 109 years but with a factor of 2 higher Martian cratering rate at ages <3 ⋅ 109 years. Those model cratering chronologies are applied to the data. The interpretation of all crater frequency data available and tractable by our methodology leads to a global Martian geological history that is characterized essentially by two epochs of activity. The division between the two epochs is measured at a cumulative crater frequency value for 1-km craters (crater retention age) of N(1) = 8 ⋅ 10-4 (km-2) corresponding to an absolute age of ca. 3 ⋅ 109 years (applying model I cratering chronology) and of ca. 1.5 ⋅ 109 years (applying model II cratering chronology). In the ancient epoch all major events like emplacement of the plains lavas, the piling up of most volcanic constructs, and large-scale erosion of channels and mensae (highland/northern lowland boundary) have taken place. During the younger epoch, only the big Tharsis shield volcanoes were active, and some minor erosion took place. This means that Mars is not a youthful planet but an ancient one with respect to most of its surface features.