(Image source)
(Image source)
From Blessed Ildefonso Schuster's The Sacramentary:
Ever since the time of St. Helen, a large portion of the true Cross has been preserved in the basilica in aedibus sessoriis... Its earliest designation was Basilica Heleniania, or more commonly Sancta Hierusalem, whence we have those frequent allusions to Jerusalem in today's Mass.
In the Middle Ages, the Pope used to proceed to the station at Sta. Croce in Gerusalemme holding in his hand a golden rose... On his return he presented it to the Prefect of Rome, and this gave rise to the custom... of sending the golden rose blessed by the Pope as a gift to one of the Catholic princes.
From the Churches of Rome wiki:
The church was consecrated about 325, in an older building that was rebuilt to house the relics. The floor was packed with soil from the Holy Land. It was at first known as the Basilica of Helena or Basilica Sessoriana (after the imperial palace that the site belonged to), but the official name was Hierusalem. The present name was given to it in the Middle Ages.
It was restored by Pope Gregory II (715–731) and Pope Hadrian I (771–795).
In 1049, the church was given to the Benedictines of Monte Cassino. They moved to San Sebastiano fuori le Mura in 1062, and the Canons Regular of San Frediano of Lucca were installed by Pope Alexander II.
The Canons of the church had it rebuilt in the Romanesque style during the pontificate of Lucius II (1144–1145).
While the papacy was based in Avignon, in the 14th century, the church was abandoned. In 1370, a few years before the papacy returned to Rome, Pope Urban V handed it over to the Carthusians. They restored the church, especially during the periods when Pedro Gonzales de Mendoza and Bernardino Lòpez de Carvajal were titulars of the church, respectively in 1484–1493 and 1495–1523.
In 1561, the Carthusians were transferred to Santa Maria degli Angeli, and Lombard Cistercians from the congregation of San Bernardo were installed. They still serve the church, but the monastery once connected to the church has been converted into barracks.
Pope Benedict XIV had it rebuilt in the Baroque style between 1741 and 1744.