Axelos was born in Athens to a doctor and a woman from an old Athenian bourgeois family, and attended high school at the French Institute and the German School of Athens. He enrolled in the law school in order to pursue studies in law and economics due to dissatisfaction with the philosophy taught at the Philosophical School of the University of Athens, but did not attend. With the onset of World War II Alexos got involved in politics. Then during the German and Italian occupation he participated in the Greek Resistance, and later on in the prelude of the Greek Civil War, as an organiser and journalist affiliated with the Communist Party (1941 – 1945). He was later expelled from the Communist Party and condemned to death by the right wing government. He was arrested and escaped.

At the end of 1945 Axelos moved to Paris, France, with around 200 other persecuted intellectuals, where he studied philosophy at the Sorbonne and lived most of his life. From 1950 to 1957 he worked as a researcher in the philosophy branch of CRNS, where he was writing his dissertations, and subsequently proceeded to work in Ecole Pratique des Hautes Etudes. From 1962 to 1973 he taught philosophy at the Sorbonne, and met Jacques Lacan, Pablo Picasso, and Martin Heidegger. His dissertation "Marx, penseur de la technique" (translated as "Marx, the Man Who Thinks Out Technique") tried to provide an understanding of modern technology based on the thought of Heidegger and Marx and was very influential in the 1960s, alongside the philosophy of Herbert Marcuse. His other dissertation was on Heraclitus, published in 1962.

Axelos was a collaborator on, columnist with, and subsequently editor of the magazine Arguments (1956 – 1962). He founded and, since 1960, has run the book series Arguments in Edition de Minuit. The journal had links to other European publications, e.g., Praxis in Yugoslavia and Das Argument in Germany, and pursued a non - sectarian Marxist approach. He has published texts mostly in French, but also in Greek and German. His most important book is "Le Jeu du Monde" (Play of the World), where Axelos argues for a pre-ontological status of play. Because of this activity and connection to major European intellectual figures, Axelos played a central role in French and European intellectual life for over 50 years.

Kostas Axelos tried to reconcile the ancient philosophers with the thinking of Marx, Nietzsche, Freud, Heidegger, and others in order to gain a new perspective on some of the problems in Marxism during his time. He avoids the charm of the fragmentary aphorisms used by Heraclitus, but uses Heraclitus' philosophy as the primary measuring stick for assessing the "positive" contribution of Marx and Engels. Axelos contributed to the growing interest of contemporary researchers in the Pre-Socratics and generally for ancient Greek philosophy, through his reading of the role of concepts in interpreting the world, which recalls Engels' Anti - Duhring..

In his dissertation Marx, the Man Who Thinks Through Technique and in his work Alienation, Techne, and Praxis in the Thought of Karl Marx, Axelos draws heavily on the Economic and Philosophical Manuscripts, reading them with the help of Heidegger and Nietzsche's concepts. He explored the consequences of "alienation" in history, such as the effects of the division of labor, private property and capital, and "externalization" of man in an "alien reality." Axelos tried to relate these descriptions of alienation to Heidegger's concept of "enframing." The latter can be lifted only with the building of communist society as a "positive appeal against private property." Then will be born the "whole man", who overcomes dualisms such as freedom and necessity, "individual and society," and the physical and the historical sciences, which are seen as false abstractions of ideology.

Following the example of his teacher Heidegger, who employed a poetic style of philosophy, Axelos often using a continuous flow of aphoristic statements to describe lists of phenomena - thus, listening to "the game of the world". Using this method to approach the "horizons of the world," Axelos decrypts the "mythological elements" of Marxism and especially criticizes tendencies toward meta - narrative that he considers nihilistic and anthropocentric (1964). Axelos' two doctoral theses and his book "Towards Planetary Thinking" (1964) were arranged as a trilogy - "The Unfolding of Errance."

Axelos continued to engage with contemporary thinking and the emerging global world by seeking to discover the "unseen horizon encircling all things" (1964), further refining his method as a continued wandering through the splintered "wholeness" that surrounds the man. To describe this state of "being - in - becoming," Axelos uses the term "the game." This is the basis of Axelos' second trilogy entitled "The Unfolding of the Game» («Le deploiement de jeu»), which includes the books: "The Game of the World" (1969), "Towards an Ethics of Problematics" (1972) and "Contribution to Logic"(1977).

Finally, Axelos' third trilogy is entitled "The Unfolding of an Investigation," and consists of the books: "Arguments of an Investigation" (1969), "Horizons of the World" (1974), and "Issues at Stake" (1979). In employing both Marx and Freud, Axelos did not carelessly reject their arguments despite trying to "liberate the vital forces" within them (1964), as his autobiography notes: "it remains to ask again, to extrapolate the Marxian and Freudian intuitions" (1997). The focus of the searches is still the "set - game of sets," especially in the context of the "end of history" debate. This is unequivocally restated as follows: "Since everything has been said and contradicted in a specific language, mainly the metaphysical language of philosophy and the language of anti - philosophy that subverts the metaphysical, is there is still something of meaning to say, and in what language?" (1974).

After completion of the third trilogy, Axelos published Open Systems (1984) as an extension of the concepts that he had hitherto employed on "exposures in the world 'with a means of capturing and writing also' the different and enormous 'wanderings' of the open world," i.e., what is not there but what is "overwhelming more people and more historical societies."

Axelos' texts were almost all written as meta - philosophical epilogues with the intention not to "passively endure our time: the inquiries that we have launched require us to look and see both near and far" (1997). The ultimate goal was to write "in a speech poetic and thoughtful, a fervent life" (1997).

Axelos' approach to thinking and philosophizing can be called 'Open Marxism,' a term Axelos himself has used. Open Marxism is an attempt to transcend the political - ideological role of Marxism and to instead "pose fruitful questions and demystify 'existing realizations.'" Axelos stressed that all kinds of action - political or otherwise - cannot be defined a priori. Axelos' thought attempts to question all forms of closure and is a form of open systems theory (as opposed to closed systems theory). Elsewhere, he called this "planetary thinking" (1964).

Axelos uses the concept of "play" both as a metaphysical category (the "system of systems") and as an ethical ideal for an unalienated society. Axelos argues, following Marx, that the opposition between work (necessity) and play (freedom) needs to be abolished, but recognizes that this would be both concrete and metaphysical. He also argues, following Heidegger, that play is the meaning of Being which has been forgotten in the modern world. The metaphysical aspect of play is what links human activity with the activity of the world, and the various systems of human life (magic, myth, religion, poetry, politics, philosophy, science) together and to the world. Thus, play is not at all a childish vocation for Axelos.