The complex lies in Istanbul, in the district of Fatih, along the Vatan Caddesi avenue, in a modern context.
In year 908 the Byzantine Admiral Konstantinos Lips, who would perish in 917 fighting against Simeon I's Bulgaria,  built a nunnery dedicated to the Virgin Theotokos ("mother of God"). The monastery, which was known also after his name (Monē tou Livos), became one of the largest of Constantinople. The church of the monastery, also dedicated to the Virgin, was built on the remains of another shrine of the sixth century.
After the Latin invasion and the restoration of the Empire, between 1286 and 1304, Empress Theodora, widow of Emperor Michael VIII Palaiologos, erected another church dedicated to St. John the Baptist (Greek: Eκκλησία του Αγίου Ιωάννου Προδρόμου του Λίβος) south of the first church. Several exponents of the imperial dynasty of the Palaiologos were buried there besides Theodora: her son Konstantinos, Empress Eirene of Montferrat and her husband Emperor Andronikos II.
During the fourteenth century an esonarthex and a parekklesion were added to this church.
In 1496, shortly after the Fall of Constantinople and under the reign of Beyazid II, the building was converted into a mosque by the Ottoman dignitary Fenarizade Alâeddin Ali Effendi, whose family belonged to the religious class of the ulema, and the monastery was converted into a dervish lodge. Since one of the head preachers of the Madrasah was named Isa ("Jesus" in Arabic and Turkish), his name was added to that of the mosque. The edifice burned down in 1633, was restored in 1636 by Grand Vizier Bayram Pasha, and burned again in 1918.  During excavations performed in 1929, 22 sarcophagi have been found.  The complex has been thoroughly restored between the 1970s and 1980s.
The Dome of the Church of St. John the BaptistThe north church has a quincuncial plan, and was one of the first shrines in Constantinople to adopt this plan, whose prototype is possibly the Nea ("New church"), erected in Constantinople in the year 881, and now lost.
The dimensions of the north church are small: the naos is 13 m long and 9.5 m wide, and was sized according to the population living in the monastery at that time. The masonry of the northern church was erected by alternating courses of bricks and small rough stone blocks. In this technique, which is typical of the Byzantine architecture of the tenth century, the bricks sink in a thick bed of mortar.
This edifice has three high apses: the central one is polygonal, and is flanked by the other two, which served as pastophoria, prothesis and diakonikon.
The apses are interrupted by triple and single lancet windows. The walls of the central arms of the naos cross have two orders of windows: the lower order has triple lancet windows, the higher semicircular windows. Two long parekklesia, each one ended by a low apse, flanks the presbytery of the naos. The angular and central bays are very slender. At the four edges of the building lies four small roof chapels, each surmounted by a cupola.
The remainders of the original decoration of this church are the bases of three of the four columns of the central bay, and many original decorating elements, which survive on the pillars of the windows and on the frame of the dome. The decoration consisted originally in marble panels and coloured tiles: the vaults were decorated with mosaics. Only spurs of it are now visible.
As a whole, the north church presents strong analogies with the Bodrum Mosque (the church of Myrelaion).
The south church is a square room surmounted by a dome, and surrounded by two deambulatoria, an esonarthex and a parekklesion (added later). The north deambulatorium is the south parekklesion of the north church. This multiplication of spaces around the central part of the church is typical of the late Palaiologian architecture: the reason of that was the need for more space for tombs, monuments erected to benefactors of the church, etc..  The central room is divided from the aisles by a triple arcade. During the mass the believers were confined in the deambulatoria, which were shallow and dark, and could barely see what happened in the central part of the church.
The masonry is composed of alternated courses of bricks and stone, typical of the late Byzantine architecture in Constantinople.
The lush decoration of the south and of the main apses (the latter is heptagonal), is made of a triple order of niches, the middle order being alternated with triple windows. The bricks are arranged to form patterns like arches, hooks, Greek frets, sun crosses, swastikas and fans. Between these patterns are white and dark red bands, alternating one course of stone with two to five of bricks. This is the first appearance of this most important decorating aspect of the Palaiologian architecture in Constantinople.
The church has an exonarthex surmounted by a gallery, which was extended to reach also the north church. The parekklesion was erected alongside the southern side of the south church, and was connected with the esonarthex, so that the room surrounds the whole complex on the west and south side. Several marble sarcophagi are placed within it.
As a whole, this complex represents a notable example of the middle and late Byzantine Architecture in Constantinople.