Founded by Zhiyi, the Chinese Buddhist school of Tiantai was developed in the 6th century AD from various aspects of Chinese Buddhism that were developing at the time. The north Chinese concentration on practice and the south Chinese concentration on scholarship were fused to create Tiantai. Tiantai held the Lotus Sutra as the most important sutra, and claimed Nagarjuna as their founding patriarch.
The Tiantai school believed in their form of existentialism, embodied in the "Three Truths": All things are empty, yet they have provisional existence, and recognizing both of these facts is the Middle Way. Tiantai belief is that Tiantai teachings are "round teachings" – they embody everything and lack sharp edges, and are therefore perfect. They allow for other Buddhist approaches to not be necessarily wrong, however they are described as only partial visions of the One True Vehicle that is Tiantai. This is a very significant part of the history of Buddhism, as it formed one of the most important and influential schools of Chinese Buddhist thought.
"Zhiyi saw samatha and vipasyana, shi and kan as the two wings of a bird in flight. In other words they should be practiced together, each informing the other. Shikan-taza, on the other hand, is the sky the bird flies in." – speech by the Venerable Shikai Woodward.
Thanks to gn0sis for pointing out that the Japanese word for Tiantai is Tendai. Tendai had changed a good deal by the time it got to Japan, but the basic ideas tried to remain the same. See Tendai for more details.