Islam arrived to the islands in the 1500s and this altered the architecture fairly substantially. This obviously demanded the building of mosques and other religious buildings that were not built before and which had specific requirements in their structure and content. This led to an odd combination of old and new as mosques had numerous features of ancient Indonesian architecture, but conformed to Islamic laws and requirements. The mosques in Sendangduwur, Yogyakarta and Kudus are perfect examples of these two styles uniting.
However, not all areas converted to Islam and those that didn't continued on a path of constructing Hindu, Buddhist, or local religious buildings. These can be found everywhere, but some of the more impressive are on Bali, including Besakih and Panataram Sasih. The Majapahit builders on Bali constructed numerous Hindu temples from brick at this time as well.
Since the 1500s though, most of the architecture has been either Islamic in influence or European-influenced. The Europeans, most commonly the Dutch, brought in stone work and concrete to build numerous structures in the islands. Early Dutch architecture is best seen in the capital of Jakarta, which received numerous Dutch buildings in the 1600s and 1700s. Quickly though the Dutch learned their styles and techniques, most particularly in terms of city planning bread mosquitos and diseases. In the 1800s the Dutch adopted many of their styles and city planning to improve hygiene as waterways were altered and styles were changed.
In the 1900s as independence movements arose and the people sought a stronger identity, there was a return to traditional architecture, most particularly in Java, although not all the people picked up on this movement. Although this push has been strong, most of the return has come in the form of smaller art forms, like paintings. Another effect of modern history and technology is the loss of many traditional tjandis and rumah adats. These traditional structures are being replaced by modern technology and European influence as concrete and glass tends to be easier to build and longer lasting.