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The contemporary theory of space-time contains a number of assumptions called invariance or symmetry principles. One of them is the principle of time-translation invariance, which expresses a symmetry property of time which is called its homogeneity. The principle of time homogeneity plays a fundamental role in physics and also has many philosophical connections. In spite of that it has not become, until now, the subject of a sufficiently broad and exact philosophical analysis. The present paper is an attempt to remove this gap. We consider here only central philosophical problems concerning the principle of time homogeneity: its physical meaning, its epistemological status, and its scope of applicability.