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Yogacara as a distinct institutional school of Buddhism is almost totally extinct. There are two temples of the Hosso sect (which is the only remaining sect of Buddhism that calls itself Yogacara) of Buddhism in Japan ( Kลf*ku-ji and Yakushi-ji) but that's really about it.
However, Yogacara as a distinct theoretical school has been preserved both in East Asia and also in Tibet. Within China, many Yogacara texts translated by Xuanzang are still read, and are incorporated into Chinese Zen.
Within Tibet, Yogacara has been preserved as part of the teachings on the different Tenet systems. Usually Yogacara is classified as being just below Madhyamaka in terms of the profundity of the view, so relatively few people accept all of its doctrines as the highest teaching, but it was very influential in a lot of meditational teachings in Mahamudra, some of the general terminology, and many in the Nyingma school combine Yogacara and Madhyamaka, using Madhyamaka as the perfect model for describing ultimate truth (i.e. emptiness) and using Yogacara as a model for describing conventional truth as all things appearing from the storehouse consciousness as a result of karma.
Also, in Tibet there is a tradition of Madhyamaka called Shentong which takes the teachings of Buddha nature as definitive, and a large amount of their vocabulary is derived from Yogacara. Some have criticised Shentong for bending certain Yogacara doctrines to make them fit, but it is a very popular interpretation within the Kagyu and Nyingma schools.
In brief, there aren't any Buddhist sects around nowadays that explicitly say "We are the Yogacara school" but the Yogacara teachings are still very much alive as a set of doctrines passed down.
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Thich Nhat Hanh uses concepts and teachings from the yogacara school and has written about it. The Book is called "Understanding Our Mind." There is also "Living Yogacara" by Shun'ei Tagawa from the Hosso School in Japan which is very insightful as well.
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See Traleg Rinpoche:
The former is for in-depth scholarly treatment, the latter book has less in-depth info for contextualization of the view in Mahamudra as influenced by Yogacara.
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Zen does. In fact, it's hugely important. Hakuin's Precious Mirror Cave (the title alone of which refers to alaya) mentions it at length; it also comes up in his verses of the Ten Kings. I wouldn't view Yogacara as a school like Shingon or Nichren is a school/tradition. Yogacara is more of a permeating idea.