Genesis
Toynbee argues that "self-determining" civilizations are born (out of more primitive societies), not due to racial or environmental factors, but as a response to challenges, such as hard country, new ground, blows and pressures from other civilizations, and penalizations. He argues that for civilizations to be born, the challenge must be a golden mean; that excessive challenge will crush the civilization, and too little challenge will cause it to stagnate.
He argues that civilizations continue to grow only when they meet one challenge only to be met by another. In 1939 Toynbee wrote 'the challenge of being called upon to create a political world-order, the framework for an economic world-order...now confronts our Modern Western society' [1]. He argues that civilizations develop in different ways due to their different environment and different approaches to the challenges they face. He argues that growth is driven by "Creative Minorities," find solutions to the challenges, which others then follow by example, called mimesis, i.e. mimeing.

Decay
He argues that the breakdown of civilizations is not caused by loss of control over the environment, over the human environment, or attacks from outside. Rather, it comes from the deterioration of the "Creative Minority," which eventually ceases to be creative and degenerates into merely a "Dominant Minority" (who forces the majority to obey without meriting obedience). He argues that creative minorities deteriorate due to a worship of their "former self," by which they become prideful, and fail to adequately address the next challenge they face.

Universal State
He argues that the ultimate sign a civilization has broken down is when the dominant minority forms a "Universal State," which stifles political creativity. He states:
First the Dominant Minority attempts to hold by force—against all right and reason—a position of inherited privilege which it has ceased to merit; and then the Proletariat repays injustice with resentment, fear with hate, and violence with violence when it executes its acts of secession. Yet the whole movement ends in positive acts of creation—and this on the part of all the actors in the tragedy of disintegration. The Dominant Minority creates a universal state, the Internal Proletariat a universal church, and the External Proletariat a bevy of barbarian war-bands.
He argues that, as civilizations decay, they form an "Internal Proletariat" and an "External Proletariat." The Internal protelariat is held in subjugation by the dominant minority inside the civilization, and grows bitter; the external proletariat exists outside the civilization in poverty and chaos, and grows envious. He argues that as civilizations decay, there is a "schism in the body social," whereby:
•abandon and self-control together replace creativity, and
•truancy and martyrdom together replace discipleship by the creative minority.
He argues that in this environment, people resort to archaism (idealization of the past), futurism (idealization of the future), detachment (removal of oneself from the realities of a decaying world), and transcendence (meeting the challenges of the decaying civilization with new insight, as a Prophet). He argues that those who Transcend during a period of social decay give birth to a new Church with new and stronger spiritual insights, around which a subsequent civilization may begin to form after the old has died.
Toynbee's use of the word 'church' refers to the collective spiritual bond of a common worship, or the same unity found in some kind of social order.

Predictions
It remains to be seen what will come of the four remaining civilizations of the 21st century: Western civilization, Islamic society, Hindu society, and the Far East. Toynbee argues two possibilities: they might all merge with Western Civilization, or Western civilization might develop a Universal State after its Time of Troubles, decay, and die.

Impact
Many concepts Toynbee discussed become part of the political vocabulary only decades later; here is a sampling of a few:
•Great Society (1939)
•régime change (1949)
•Détente (1952)
•malaise (1956).
The Intercollegiate Studies Institute listed A Study of History as #5 in its 50 Best Books of the Twentieth Century in 2001.

Criticism
The social scientist Ashley Montagu assembled 29 other historians' articles to form a symposium on Toynbee's A Study of History, published as Toynbee and History: Critical Essays and Reviews, 1956 Cloth, Boston: Extending Horizons Books, Porter Sargent Publishers. ISBN 0-87558-026-2.  The book includes three of Toynbee's own essays: What I am Trying to Do (originally published in International Affairs vol. 31, 1955; What the Book is For: How the Book Took Shape (a pamphlet written upon completion of the final volumes of A Study of History) and a comment written in response to the articles by Edward Fiess and Pieter Geyl (originally published in Journal of the History of Ideas, vol. 16, 1955.)
Arnold Toynbee suggests that the civilisation as a whole is the proper unit for the study of history, not the nation state, which he suggests is just a part of a larger whole. He suggests a list of 21 civilisations, and an additional 5 "arrested civilisations", but when one examines this list it seems to be very arbitrary at times where one civlisation ends and a new one starts. For example, do we identify a "Sumerian" civilisation in ancient Iraq, followed by a later "Akkadian, or Babylonian" civilisation, or are these just different phases of a single, long-lived Mesopotamian civilisation? Toynbee lists them as separate, but later includes both the Greek and the Roman civilisations within a single category, called "Hellenic," though it is clear from Toynbee's list that Greek gave rise to Roman just as Sumer gave rise to Babylonia. Why is Sparta listed as a separate civilisation from the rest of the Hellenic world? What is the relation between Minoan and Mycenaean (which Toynbee considers early Hellenic). Jacquetta Hawkes considers these two aspects of the same civilisation (which she calls Mino-Mycenaean, a finding that would be supported by Leonard Palmer from his studies of Linear B). If these are just early phases of a much larger civilisation, separated from Hellenic civilisation by a "Dark Age", what is one to do with what Toynbee calls "Sinic civilisation", separated from "Far Eastern Civilisation", or for that matter "Indic civilisation" separated from "Hindu civilisation"? And in his list there is no mention of such civilisations as the Etruscans, the Ethiopians, the East Africans, or the Sudanese. (While the latter could perhaps be considered part of the Islamic civilisation, the former could not.) And what of Tibet and South East Asia (old Indo-China), are they part of the Indian Hindu Civilisation even though they are Buddhist, or part of Far Eastern Civilisation, or both. And if Hittite is a separate civilisation, where do Hurrians, Elamites and Urartu fit?
David Wilkinson suggests that there is an even larger unit than civilisation. Using the ideas drawn from "World Systems Theory" he suggests that since at least 1500 BCE that there was a connection established between a number of formerly separate civilisations to form a single interacting "Central Civilisation", which expanded to include formerly separate civilisations such as India, the Far East, and eventually Western Europe and the Americas into a single "World System". This idea has much to recommend it. In some ways it resembles what William H. McNeill calls "the closure of the oecumene", in his book The Rise of the West.
And then concerning the fall of civilisations, Toynbee suggests a single schema, drawn in part from his experience as a classical scholar, based upon the creativity of classical Athens, and the rise and fall of the Roman Empire. This pattern he finds has parallels with Sima Qian's views of the "Mandate of Heaven" or the Dynastic cycle suggested by Ibn Khaldun, for Far Eastern and Islamic civilisations respectively. But the pattern is not universally observed, and a number of civilisations become incorporated into others. These he suggests are the so-called Aborted civilisations. It is interesting that Ireland (a far Western Christian) and Scandinavia (the Vikings) are called abortive, when they contributed so heavily to the independent Western civilisation, whilst pre-Muslim Ghana is not considered at all.