The Buddha was Indian, and for the first few hundred years of its existence, Buddhism was largely confined to India. With the adoption of Buddhism by Ashoka, the 3rd ruler of the Mauryan Empire, who expanded the empire to cover most of modern India, Pakistan, and Bangladesh, Buddhism gained a powerful supporter, and became a prominent Indian religion. This was in the mid 3rd century BC, when Buddhism was perhaps about 250 years old. Supported by Ashoka, Buddhism spread outside India, to Sri Lanka and Central Asia, including the Seleucid Empire. Buddhism became an important religion in what is now Afghanistan, Iran, Uzbekistan, Turkmenistan, Tajikistan, and Kyrgyzstan. From Central Asia, Buddhism spread along the Silk Road to China, and from China to Korea and Japan.

Buddhism also spread to SE Asia (Burma, Thailand, Cambodia, Laos, Malaya, Indonesia) directly from India. These two main routes of spread were dominated by two major branches of Buddhism - Mahayana Buddhism via the Silk Road to China, and Theravada Buddhism from India directly to SE Asia.

Then the western portion of the Buddhist world largely ceased to be Buddhist, leaving continental SE Asia, China, Tibet, Japan, Korea, and Mongolia as the strongholds of Buddhism. The decline of Buddhism in Central Asia is straightforward: the Islamic conquests, and the subsequent spread of Islam to Turkic peoples such as the Uyghurs led to the dominance of Islam in Central Asia at the expense of Buddhism and other religions such as Zoroastrianism.

The decline of Buddhism in India appears to have been multi-faceted, with the exchange of ideas between Hinduism and Buddhism leading to new and vigorously growing forms of Hinduism such as monotheistic Vaishnavism (with the single deity appearing in many forms; this has been called "polymorphic monotheism") which obtained the state support that Buddhism had formerly enjoyed (and thus, Buddhism lost that state support). The conquest of northern India by Islamic rulers further eroded Buddhism. Buddhism still exists in India, with about 10,000,000 adherents - a large number in total, but a tiny fraction of the Indian population, and a tiny fraction of world Buddhism.

The spread of Islam into SE Asia was also at the expense of Buddhism, with Buddhism (and/or Hinduism) largely replaced in Indonesia and Malaya (with some survivals).

For a map showing the spread and retreat of Buddhism, see

• https://commons.wikimedia.org/wiki/File:Buddhist_Expansion.svg

Notable is the light yellow regions in Central Asia, India, and Indonesia/Malaya, where Buddhism had previously been an important religion, but was largely replaced by Islam and resurgent Hinduism. This map overstates the extent of Buddhism in China - Xinjiang in the far west of China (north of Tibet) is predominantly Moslem. For a more accurate religious picture of China, see https://commons.wikimedia.org/wiki/File:Map_of_Religions_in_China.png