I was reading this Wikipedia page and it lists terrorist attacks motivated by Islamic fundamentalism from 1979 onwards. Before that, most terrorist attacks seemed to be inspired by nationalism and political reasons, such as Communist and Anti-Communist groups in Latin America and even in the Middle East, including Palestinian organizations like the Black September (from the 1972 Munich attack).
Violent Islamist groups have employed terrorist tactics almost from the outset.
The Islamist group ne plus ultra, the Muslim Brotherhood was founded in 1928 in Egypt by Hassan al-Banna. By 1936 the Brotherhood made use of paramilitary "rovers", roughly styled on Fascist Brown/Blackshirts who in Egypt as in Europe fought street battles with their communist and other political rivals. At some point in 1942/43 he founded the violent "Secret Apparatus", which was charged with being able to carry out bombings and assassinations.
In 1948 they carried out a series of bombings against Egypt's Jews, killing 70 and injuring another 200 in Cairo alone. Also in 1948, a Brotherhood member assassinated Egypt's Prime Minister Mahmoud Nukrashi. This in turn led to al-Banna's assassination in 1949.
After decades of repression, the Egyptian Brotherhood officially renounced violence in the 1970s.
In general, the 1950s, 60s and 70s were not a particularly great time for Islamist groups generally. The ideological bent of the entire region was being driven by pan-Arabism, Socialism, and Nationalism. That doesn't necessarily mean these groups were un-Islamic. The Algerian FLN employed terrorist tactics in the Algerian war of independence and Islam was a key part of their ideology, but no one would describe the FLN as an Islamist group per se.
1979 was, however, a watershed year in Islamism re-emerging a powerful transnational force and in the development of contemporary terrorism. The Islamic revolution in Iran inspired would-be Islamists around the world. The tactical use of explosives in martyrdom operations was a development that emerged out of the Iran-Iraq war. The eventual impact of the Soviet invasion of Afghanistan is well known. Egypt's peace deal with Israel meant that Egyptian style Arab Nationalism would no longer be the primary vehicle for opposing Israel. The seizure of the Grand Mosque of Mecca convinced the Saudis of the need to begin a program of pushing internal problems outwards by exporting their religious ideology.
A number of seminal groups most prominently associated with contemporary Islamist terrorism were founded shortly thereafter. Osama bin Laden goes to Pakistan in 1979. International branches of the Muslim Brotherhood begin helping to organize the Afghan Jihad. Egyptian Islamic Jihad, whose most famous member was Ayman al-Zawahiri, was founded in 1980. Though the precise date of its formation is disputed, Hezbollah was founded in the early 1980s. Hamas was founded in 1987. And so on.
Short Version:
-> Islam enters the global Political world in a major fashion.
The Long version:
A rather difficult question since the Islamic world stretches halfway across 2 of the biggest continents and a small pocket in Europe. The situation for Afghanistan is diffrent then for Zanzibar. But in general, after the decolonisation countries were founded based on the colonial borders bringing diffrent ethnic (and even religous) groups together. The best example are perhaps Syria and Iraq on the ancient border between the Arab (mainly Sunni Islam), Turkish (mainly Sunni) and the Persian (mainly Shiite) worlds. . In some countries like Marocco, which kept it's royal family and had been an actual country for atleast 300 years, this transition was easier. Others like the formentioned Iraq and Syria on the other hand this was more difficult. The era of colonisation was looked upon as a time of shame and the, often military, leaders of these new countries used nationalism to forge/bind these new states.
These new countries had to be strong and Westernisation was considerd the way forward. Although the capital and major cities changed drasticly the rural (and more populous) regions were often left behind causing a rift between the lifestyle of the urban elite/middle class and the countryside.
Most counties would seek help from the Western Nations, although a few turned to the USSR. Both of them were happy to support anyone in their cold war and the result is often the same. Foreign companies/states gain acces to resources and due to the kleptocratic nature of these regimes the benefits go largely to to the ruling class. In these conditions the foundation for a healthy economy is destroyed and the ever-growing population is kept in check on one hand by low food and energy prices and on the other hand by a severe crackdown on any political opposition. (which can easily be framed as pro-communist in regimes supported by the west and vice-versa)
The late 50's and early 60's were dominated by the idea of Pan-Arabianism, in which the Egypt of Nasser, was the frontrunner. His fame was cemented by the '56 Suez Crisis which, although they lost on the battlefield, was a major political victory.
will be continued.... (it's bit too late to carry on atm)
Sources:
PS: This is my second post in this subreddit, my first one got deleted because it didn't follow the rules. If I didn't follow the rules this time please do not delete this post but tell me what I did wrong.