Short answers, pulled from the story.
The Zhenyan tradition of Chinese Esoteric Buddhism was established between 716 and 720 by three Indian masters: Śubhakarasiṃha, Vajrabodhi, and Amoghavajra, during the reign of Emperor Xuanzong of Tang. Scholar Geoffrey C. Goble considers Amoghavajra the most influential of the three and the true founder of the Mantra Tradition.
Amoghavajra remained in Chang'an when it was occupied by An Lushan's forces in 756 and performed Vajrayana rituals intended to bring death and disaster upon the rebels. He also passed secret military intelligence to the Tang crown prince Li Heng. After the rebellion was suppressed, Emperor Suzong was crowned cakravartin by Amoghavajra in 759, and Esoteric Buddhism was recognized as the official state Buddhist sect.
The Japanese monk Kūkai, known as Kōbō Daishi and born in 774, traveled to Tang China and studied under Master Huiguo. He returned to Japan and established Shingon Buddhism at Tō-ji temple in Kyoto. A parallel transmission by Saichō, who lived from 767 to 822, became Japanese Tendai, known as Taimitsu. These two schools, Tōmitsu and Taimitsu, became the two main forms of Esoteric Buddhism in Japan.
The Three Mysteries, known in Chinese as Sānmì, are the secrets of body, speech, and mind. They correspond to the three modes of ritual action: mudra (hand gesture), mantra (sacred sound), and mandala (sacred diagram). Through the abhiseka initiation, a practitioner uses these three modes to ritually replicate the body, speech, and mind of the Buddha.
After the Mongols established the Yuan dynasty in 1271, they made Tibetan Buddhism the official religion of China, reflecting their prior conversion to the faith under Mongol rule. Lamas of the Sakya and Kagyu schools served as imperial preceptors, the tantric deity Mahakala became the protector of the Yuan state, and Tibetan monks received unprecedented patronage at court.
The Neo-Zhenyan revival is an ongoing effort, centered in China, Taiwan, and other East Asian countries with Chinese populations, to restore Tang-era Esoteric Buddhism. It is led mainly by Chinese monks and laypersons who travel to Mount Kōya in Japan, receive training and dharma transmission as acharyas in the Shingon tradition, and return home to teach. Sites like Qinglong Temple and Daxingshan Temple in Xi'an are among the revival's focal points.