In the Coptic tradition, the night vigil is kept by the chanting of the Midnight Praises, known in Arabic as the tasbeha (from tasbih, 'praise'). The tasbeha includes the canticles (probably better known in the Church by their Coptic name, hoos) and the explanations of the canticles (Coptic: lobsh), the Psalis, the Theotokias, the commemoration of the saints, the gospel reading, and some other hymns that are categorized one way or another that I honestly cannot remember (I've only performed tasbeha once, when I was in the monastery doing the fieldwork for my master's degree; my own parish was too small for it, but I know others will gather to perform it).
There is also in the Agpeya/Horologion the Prayer of the Veil, to be prayed by monks after the Compline/retiring prayer.
From memory (this was almost 5 years ago now), in the monastery we would pray the Compline prayer and then be excused for rest for a few hours (I assume that the monks prayed the Veil at this time, but I don't know because I rested in another room) to rise c. 10 pm for the tasbeha, which lasted until 1 am, and then we went to sleep to rise for the morning prayer c. 6 am.