When it comes to understanding Greek philosophy, it is of vital importance to clarify the concepts used by philosophers. But the desired clarity is hard to achieve in general for pre-Socratic, and in particular for Anaximander’s philosophy. The reason for this difficulty is the fact that the interpreters attach to an Aristotelian perspective as well as the inadequacy and disjointedness of the surviving fragments. This study focuses on four problems arising from these interpretations: a) Did Anaximander take apeiron as an arche in common with the Aristotelian perspective? Or could there be some other meaning of it? b) Is it possible, in interpreting apeiron, to go beyond this Aristotelian understanding by maintaining the abovementioned possibility? c) What is the relationship or rupture between khaos and apeiron? In addition to this question, is it possible to place Anaximander at the centre of the mythos-logos break that is traditionally stated in Greek philosophy? d) Is it possible to evaluate apeiron by taking into consideration its political implications? A binding response to the afore-mentioned problems does not seem feasible due to the lack of fragments to give precision. For this reason the responses to each of these problems are discussed and it is tried to show how these responses are based on the possible interpretations of apeiron.