The Indian Subcontinent
The history of Islamic conquest and rule in Indian Subcontinent, including Pakistan and Bangladesh – depending on the source you consult – is either the natural advance of peaceful rule enabled by pre-existing trade routes, or the greatest holocaust and centuries long genocide the world has ever known. 
Where is the truth? Given what we know about how Islam was spread militarily in the Middle East and Africa, it’s hard to imagine a “benign colonialism” leaving society and existing religions alone and unmolested.
Today Islam is the second largest religion in India, with 14.2% of the country’s population or roughly 172 million people identifying as adherents of Islam (2011 census). Islam first came to the western coast of India when Arab traders as early as the 7th century CE came to coastal Malabar and Konkan–Gujarat. Cheraman Juma Mosque in Kerala is thought to be the first mosque in India, built in 629 CE by Malik Deenar. Following an expedition by the governor of Bahrain to Bharuchin the 7th century CE, immigrant Arab and Persian trading communities from South Arabia and the Persian Gulf began settling in coastal Gujarat.Ismaili Shia Islam was introduced to Gujarat in the second half of the 11th century, when Fatimid Imam Al-Mustansir Billah sent missionaries to Gujarat in 467 AH/1073 CE. Islam arrived in North India in the 12th century via the Turkic invasions and has since become a part of India’s religious and cultural heritage. (from Wikipedia).
But the history of Islam here is complicated and comprehensive. Muslim conquest and rule over Indian society began in 642AD and continued over a thousand years. It wasn’t until the Ottoman Empire’s decline in the early 19th Century did Islam’s grip lessen. And, in short order, the inhabitants of the Subcontinent saw rule essentially transfer from the Caliphate to the new global naval power – the United Kingdom. Here’s a timeline of the major Muslim ruling empires, sultanates and dynasties over India:
- 7th and 8th Centuries – The Umayyad Dynasty
- 13th to 16th Centuries – The Delhi Sultanate
- 14th to 15th Centuries – Timur
- 16th to 19th Centuries – The Mughal Empire
- 18th to 19th Centuries – The Durrani (Afghan) Empire
- 17th to 19th Centuries – The Maratha Empire
This post cannot possibly do justice to the thousand year + history of Islam in India. But for reference, one should start by reading the following: here, here and here.
Southeast Asia
Often called the “Muslim archipelago,” Southeast Asia is one of the most populous parts of the Islamic world. There are more than 240 million Muslims in this sub-region of Asia, counting for about 42 per cent of the total Southeast Asian population, or about 25 per cent of the total world Muslim population estimated at 1.6 billion. The majority of Muslims in Southeast Asia belongs to the Sunni (Sunnite) branch of Islam, and follows the Shafii school of Muslim jurisprudence. [Source: Oxford Islamic Studies Online, viewed in August 2014]. Islam is the official religion of Malaysia and Brunei, and is one of the officially recognized religions of Indonesia, Thailand, and the Philippines. Southeast Asian Muslims come from many ethnic groups, speaking different languages such as Bahasa Indonesia, Malay, Javanese, Maranao, Maguindanao, Tausug, Thai, Chineseand Burmese.
Historically, it is not exactly clear when Islam came to Southeast Asia, and whether Muslim Arabs, Persians or Indians, etc. were its main disseminators. But there is little doubt that it was spread for the most part by merchants in the 12th century. Traders and preachers from Gujarat in India and China navigated the waters of the Indian Ocean, the Straits of Malacca, the Gulf of Siam, and the South China Sea. The 13th century saw the establishment of the first Islamic kingdom, in Pasai in Sumatra.
In the 12th century, the Indian Chola navy crossed the ocean and attacked the Srivijaya kingdom of Sangrama Vijayatunga Varman in Kadaram (Kedah). The capital of the powerful maritime kingdom was sacked and the king was taken captive. Along with Kadaram, Pannai in present-day Sumatra and Malaiyur and the Malayan peninsula were attacked. Soon after, the King of Kedah Phra Ong Mahawangsa became the first ruler to abandon the traditional Hindu faith and converted to Islam with the Sultanate of Kedahestablished in year 1136. Samudera Pasai converted to Islam in the year 1267. The King of Malacca Parameswara married the princess of Pasai, and their son became the first sultan of Malacca. Soon Malacca became the centre of Islamic study and maritime trade; other rulers followed suit.
When Marco Polo visited the area in 1292 he noted that the urban port state of Perlak was Muslim, Chinese sources record the presence of a Muslim delegation to the emperor from the Kingdom of Samudra (Pasai) in 1282, other accounts provide instances of Muslim communities present in the Melayu Kingdom for the same time period while others record the presence of Muslim Chinese traders from provinces such as Fujian. The spread of Islam generally followed the trade routes east through the primarily Buddhist region and a half century later in the Malacca‘s we see the first dynasty arise in the form of the Sultanate of Malacca at the far end of the Archipelago form by the conversion of one Parameswara Dewa Shah into a Muslim and the adoption of the name Muhammad Iskandar Shah after his marriage to a daughter of the ruler of Pasai. In 1380, Sufi orders carried Islam from here on to Mindanao.
By the end of the 15th century, several areas of northern Sumatra, including what is now Java, were governed by Muslim rulers. It wasn’t until 1641 that the first Sultan took their title in what is now Java. Islam initially arrived on the coast of Sumatra, and spread down and around the coast to the Malacca strait and jumped across the straight to the Malay Peninsula.
In 1511, the Portuguese took over Malacca, but various other Muslim states began to grow in size and economic and political prominence. For example, Aceh dominated the region, both politically and economically, in the early seventeenth century. Through familial and trade relationships in these Muslim states, non-Islam states were slowly exposed to the faith. As it spread, Islam encountered pre-existing spiritual beliefs —including Buddhism and Hinduism —which continued to be practiced alongside Islam or were incorporated into Islam. Indeed, the faith introduced by some of the religious merchants was Sufism, a mystical version of Islam that is rejected by more conservative Muslims. Islamic law was also formally practiced in most areas that had encountered Islam, affecting cultural practices.
There are several theories to the Islamization process in Southeast Asia. The first theory is trade. The expansion of trade among West Asia, India and Southeast Asia helped the spread of the religion as Muslim traders brought Islam to the region. The second theory is the role of missionaries or Sufis. The Sufi missionaries played a significant role in spreading the faith by synchronizing Islamic ideas with existing local beliefs and religious notions. Finally, the ruling classes embraced Islam which further aided the permeation of the religion throughout the region. The ruler of the region’s most important port, Malacca Sultanate, embraced Islam in the 15th century, heralding a period of accelerated conversion of Islam throughout the region as the religion provided a unifying force among the ruling and trading classes near mister man. The word daulat refers to the legitimacy of a ruler, through the power of God, and suggests the strong relationship between rule, legitimacy, and the spread of Islam.
By the time othe Portuguese arrived in the early 16th century, Islam had a firm footing in maritime Southeast Asia. This continued to develop in the 17th century, when Arab traders and scholars/holy men from Hadramawt (a.k.a. Hadhramout and Hadhramaut, Southern Arabia) settled in the area.
These merchant missionaries introduced Sufism, a form of Islamic mysticism frowned upon by conservative dogmatic and doctrinaire Muslims. (source)