The Crescent Falls:
A world in which the Muslims were defeated by the Sassanid Persians at the battle of Al-Qadisiyahh and routed. With their army routed and most of their leaders killed in the battle, the Caliphate was forced out of Iraq and back into Arabia. With their defeat also ended the forcible spread of the new religion Islam by conquest. Butterflies flapped in every direction from the victory.
The Persian Empire survived under the Sassanid Dynasty for a few more centuries whilst Christians continued to multiply within their empire and spread into Central Asia and further. However their empire came to an end when the Turks came charging through the region and brought their empire down. The Persians have waxed and waned over the centuries under several different dynasties but have always survived and even assimilated their invaders. Persia today is a fairly modern state that managed to keep up with the technological advances of Europe and East Asia. Their rich oil deposits helped especially with their modernisation and they are now a fairly powerful state even if they do not exert any power over other states. The empire did eventually convert to Christianity but it incorporates numerous aspects of Zoroastrianism and creates a lot of hostility with the more orthodox forms of Christianity, many of whom do not accept it as a proper branch of the religion.
There was no Arabization of North Africa but things did change. The Berbers did migrate and replace most of the Latin and indigenous peoples. The Imazighen built a mighty empire that stretched across much of the West African Coast before the Europeans arrived. A rump kingdom has survived and still claims the legacy of their old empire. Much of North Africa still speaks Latin derived languages with mixtures of Berber. The Roman Empire has established several client states out of North Africa and colonised most of the Sahara region.
The Roman Empire is a large Greek speaking state. The Roman Empire survived and waxed and waned over the centuries, endured further Slavic incursions and the invasions of the Turks but they always bounced back. A cultural Renaissance eventually took place in the Middle Ages, and the Romans were the first state to discover a form of scientific method based on Greek philosophy and discoveries. Today the Roman Empire is a vast and complex entity, composed of numerous autonomous provinces and client states. The Empire has become an unwieldy behemoth because of it but it has kept the Empire together. The Romans revived a lot of concepts from Classical Greece including democracy first of the Athenian variety and later the Roman. Male suffrage is universal and even property owning women are qualified for the vote. The Emperor does have more power than an OTL constitutional monarch but his powers are definitely constrained by the Senate. The Greeks have valued technological advancement and speculation for centuries now and most higher technology is produced here as well as the theoretical sciences. Their artistic revival has given them a bit of a reputation as flowery poets amongst their more aggressive or abrasive neighbours and rivals.
Despite the absence of a Muslim invasion, a Holy Roman Empire did eventually coalesce amongst the Germanic kingdoms of Europe. Like OTL there was an intermingling of Germanic and Latin as they spread into the Mediterranean. Without Islam to provide a unifying factor Christianity remained somewhat more fractured amongst western and northern Europe. Like the Roman Empire in the east the Holy Roman Empire served as the reinforcing figure for the church but this also served to dissuade those who opposed the empire from remaining in the Catholic Church. For a long time Rome was in their possession as was the Papacy. The Holy Roman Empire survived as a more centralised state than OTL though it would ultimately expand and shrink over the centuries. Italy and thus Rome was lost to the Roman Empire and after the democratic uprisings so was 'Germany' and many of their European possessions seceded. The European territories of the Holy Roman Empire are now centred in the British Isles, the Netherlands and western France. However overseas they still rule a mighty colonial empire that they had the benefit of arriving on first (more or less). Whilst the Roman Empire decentralised to satisfy their people the Holy Roman Empire instead chose to centralise theirs. Other cultures in their empire have either been assimilated or are in he process of being assimilated through re-education and slow cultural destruction. The empire itself is still governed under a multi-tiered system but all of it answers to a single central authority. Still possessing the Papacy (in exile) means that Catholicism, in a somewhat more ATL form, is the only official religion and conversion missions are common. This of course causes problems in the areas of their empire that follow other Christian denominations. By this point there are few that are not Christians. Everything in this empire is managed by a gargantuan bureaucracy spread across the empire. Modern technology has made communication between the various bureaus more efficient and has also made monitoring others easier. However there are those who (supposedly) watch the watchman and everyone is held accountable for corruption if their supervisors can prove it.
The ATL Renaissance from the Balkans did reach Europe. The Holy Roman Empire did disagree with a few of the new ideas that begun to circulate as a result of it and attempted to crack down on it. This simply produced more radicals, dissidents and rebels. The centuries went by until the people of the German states rebelled against the empire. They embraced Roman democracy in its Classical form and the revolution spread across Central and Eastern Europe. The Federal 'Germanic' Republic is the most powerful of these states and also the most technologically advanced. The new capital of Malemberg is a scientifically designed city with wide avenues of evenly spaced and distributed buildings. The city is organised into functionally specific districts all connected by a road and rail system that runs on time thanks to the latest in computer technology. Various other republics form the Bloc. Republicanism often employs certain degrees of rationalism and technocratic ideas and whilst the degrees to which the various republics adhere to them differ, it is still a defining characteristic of the Bloc. Religion is still a facet of the Bloc but all the nations are now strictly secular and fairly tolerant of other religions. Atheism is common and often endorsed by the more rationalist regimes as is agnosticism. However despite the best attempts of numerous politicians, the Bloc still remains a loose entity with very few unified institutions or initiatives between the member states besides their economic policy, open borders and shared ideology base.
Arabia was passed back and forth between various conquerors. Whilst Islam did survive the defeat its expansion was halted and soon enough the people of Arabia were converted, often forcibly, by the Christian powers that invaded. Islam today is a minority religion practised in the more isolated regions of the peninsula or a often persecuted diaspora scattered across the Indian Ocean. Africa is now decolonised by most powers. These days influence is largely exercised by proxy through the local regimes that have sprung up in the wake of the European withdrawal. Like OTL Africa did suffer through the revival of slavery, which lasted longer than OTL and was then colonised by the world powers though there was a different cast of characters who did it. Several African states managed to remain independent and many have since come into their own. However much of the continent is still in chaos with poverty, kleptocracy and general anarchy being very common.
The Indian continent did a somewhat better job of staying on top of modern technology and a significant portion of it held off colonialism by other powers. The Empire of Mauthrayas was headed by a somewhat more progressive dynasty and happily introduced European and Asian technology and adopted several developments during the industrial revolution. The Indian subcontinent never gained a European technology is divided between the Hindu and Buddhist religions with a Christian/Manichean minority in the western portion of the subcontinent. Mauthrayas is still relatively backward compared to the other great powers of the world but they are rapidly industrialising. They have now begun to compete with the Chinese to produce the highest quantity of cheap consumer goods on the planet.
China received a very different history thanks to the changes in the migration patterns of the tribes of Central Asia. Butterflies saw very different figures take the helm of the Chinese. China remained far more open to the world and much like India picked up a few more technological innovations from the Europeans whilst adding a few indigenous techniques and discoveries of their own. Today China is a mighty and advanced empire with an enormous population and great prestige across the world. Despite continuing their sea travel and explorations the Chinese never invested in colonialism like the Europeans and did focus more on their own lands. However this has allowed them to not only avoid any conquest attempts from Europeans but also given them the means to hold onto most of their own vassal states as well. The Emperor is still an absolute ruler but courtly protocol and the labyrinthine bureaucracy make any decision making on his part almost impossible. Their large population base has also allowed them to make a niche for themselves as the manufacturing centre of the world. Millions of tonnes of mass produced goods flood out of the coastal cities and across the world making China the economic heart of much of the world.
Thanks to a wider Renaissance and Industrial Revolution as well as the cross-cultural exchange of European and Asian innovations, technology is more advanced than OTL. The developed world is also larger as well and the standard of living in places such as East Asia and South America is higher as well. Socially this world is far more authoritarian due to a very different Renaissance that spread a different set of ideas and values. Imperialism and Enlightened Absolutism are still alive and well and even the Republican Bloc is very authoritarian and controlling of its population. There was only one global industrial war over territories in Africa in the 1940s between the Republican Bloc and the two Roman Empires that eventually dragged a few more players into the quagmire. This war was even more devastating thanks to the more advanced technological package of the time. This war also brought nuclear weapons into existence and several primitive models were even used by the opposing power blocs. Since then an ATL version of Mutually Assured Destruction has been keeping a tenuous sense of global peace (excusing proxy wars) and the two blocs even began a period of Détente in the 1980s.