The article is dedicated to the problem of relevance of the Classical Greek understanding of philosophy to contemporary philosophy. A distinction is made between the relevance of the Greek philosophy that has already been realized, or made actual, in the sphere of contemporary philosophy and culture, and the relevance of the Greek philosophy which is yet in need of realization, that is, which has a potential of being realized in the future. The author, mainly focusing on this latter kind of relevance, for it is more interesting from the philosophical point of view and suggests new ways to reinvigorate the contemporary field of philosophical thought, discusses the original Greek understanding of philosophy that can be discerned from the ancient Greek philosophical texts and the original Greek term for philosophy, philosophia. The author presents an analysis of the Greek word philosophia from the etymological and conceptual points of view, disclosing its several layers of meaning. It is argued that the Greek philosophical thinking employs a productive combination of pre-methodical and methodical thought, deriving from this combination a specific synergy that might also be useful to contemporary philosophy. A point is made that the original Greek notion of philosophy, understood as the love of divine wisdom, presupposes both modesty, stemming from the acknowledgment of one’s absolute ignorance of the most important philosophical answers, and intellectual passion. The author makes a claim that the original close and deep relation between the Greek philosophy and astronomy was instrumental in the original Greek understanding of the philosopher as a theōros of a special kind, that is, as a theoretic viewer of the entire cosmos who focuses on the whole of the cosmos (or reality in general), not on its individual constituents and details. What was expected of the Greek philosopher was the ability to deeply appreciate the beauty, unity, and underlying divine order of the cosmos, not the capacity to acquire the knowledge of concrete information related to it. The attention is drawn to the circumstance that the Greek philosopher’s aesthetic appreciation of the cosmos that took place at the moments of its theoretical contemplation had also a specific ethical aspect to it – an aspect that cannot be simply explained in terms of the Classical Greek virtue ethics and can be rather viewed in terms of the modern approaches to ethics. The relation between the ability to acknowledge one’s ignorance of the most important matters and the capacity to theoretically contemplate and aesthetically appreciate the cosmos in holistic terms is viewed by the author as potentially relevant to those contemporary thinkers who seek to reassert the unique status of philosophy, its special place among other disciplines, and to rethink the radical difference between philosophy and science. After discussing some other aspects of potential relevance of the Greek understanding of philosophy to contemporary philosophy, the author makes a conclusion that the Classical Greek understanding of the nature of philosophy should be viewed not as having to replace, but as being able to complement the current understanding of the nature and mission of philosophy.