Scholars and philosophers of religion have tended to see Hinduism as an ethnic religion, a religion of a particular people and associated with their land or place. According to this view, a person was a Hindu by virtue of his or her birth in a Hindu caste. Such a person, by traditon, was then subject to the dharma of his or her community, station in life or ashrama, and its rules and customs.
The realm of dharma, the Hindu Universe, was known as Bharat, the land we call India (Bharat is the original name of this land, named after Bharatha, one of the brothers of Lord Rama).
Historically, the spread of Hinduism came via the travels of merchants to other nearby countries for business. The Chettiars (var. Chettyars), a Tamil banking community, extended their business to Burma, Malaysia, Mauritius and other parts of South East Asia. Additionally, strong trading links have existed for centuries between Western India and East Africa. It was Mahatama Gandhi, who, upon completing his law degree, left India to practice in South Africa, and commenced his famous life task of sathyagraha, non-violent protest after he was told he could not travel in a first class carriage on a train, and was made to move to third class.
In 1893, Swami Vivekananda attended the World Parliament of Religions in Chicago, and thereafter was deluged with requests to teach in the USA and in Europe. Paramahansa Yogananda settled in the USA in 1920 and founded a branch of the Self Realisation Fellowship there. He wrote Autobiography of a Yogi, which has remained one of the modern spiritual classics.
In the 1960's and 1970's, the fame of the Maharishi Mahesh Yogi spread throughout the world, and moreso when he was visited by the Beatles. Another Hindu ambassador was the founder of what is called the Hare Krishna's, Bhaktivedanta Prabhupada, when he showed up in New York City in 1970 and began to attact devotees and disciples. Many other gurus lived in the US, and those who did not, established foundations there, such as Swami Muktananda, Shree Maa of Kamkhya, Anandi Ma, and the Self Realisation Fellowship of Paramahansa Yogananda spread to the rest of the world.
In modern times, other Hindu divines have lived in other countries of visited them. Mother Meera of Andhra Pradesh, India, lives Frankfurt, Germany and travels to the US to visit schools and devotees; Anandamaya Ma attracted devotees worldwide, and Amritanandamayi Ma (Ammachi - the Hugging Saint) travels the world regularly to visit devotees and ashrams established by her order outside India.
Hindu enclaves in various countries have also become established due the export of talented computer developers who (mostly) have a foundation in Vedic mathematics, which enables a ease of use with development languages and computer architecture. Wherever Hindu's go, they take their faith, their rituals and establish temples and communities. Large enclaves of Hindus may be found in the UK, the US, Fiji, Mauritius, Malaysia, and South Africa.