Their story
Adapted in modern English from the Catholic Encyclopedia (1913) · original text below
Eutychianus succeeded Pope Felix I a few days after Felix's death and led the Church from January 275 until 7 December 283. Nothing is known of the details of his pontificate.
The Liber Pontificalis (the early medieval 'Book of the Popes', not always reliable for the earliest ones) credits him with a rite for blessing the produce of the fields, but that rite clearly belongs to a later period. It also says he made rules for burying martyrs and buried many with his own hands, but this is doubtful, since the Church had a long rest from persecution after the death of Aurelian in 275. He probably did not die a martyr: the fourth-century Roman Calendar lists him among the bishops, not the martyrs. He was laid in the papal chapel in the Catacomb of Callistus, where fragments of his epitaph were found, his name in Greek letters with the word for bishop. His feast is 8 December.
From the Catholic Encyclopedia
1913 · 185 words
Eutychianus [followers of Eutyches, who said Christ had only a divine nature; condemned at Chalcedon in 451], Saint, Pope. He succeeded Pope Felix I a few days after the latter's death, and governed the Church from January, 275, until December 7, 283. We know no details of his pontificate. The rite for blessing the produce of the fields, ascribed to him by the "Liber Pontificalis", undoubtedly belongs to a later period. The statement also that he promulgated rules for the burial of martyrs and buried many of them with his own hands, has but slight claim to acceptance, since after the death of Aurelian [Roman emperor 270–275] (275) the Church enjoyed a long respite from persecution. It is highly probable that Eutychianus did not die a martyr. The fourth-century Roman Calendar mentions him (December 8) in the "Depositio Episcoporum", but not in its list of martyrs. His remains were placed in the papal chapel in the Catacomb of Callistus. When this famous crypt was discovered the fragments of the epitaph of Eutychianus were found, i.e. his name (in Greek letters): EUTYCHIANOS EPIS (KOPOS). His feast is celebrated on December 8.
Duchesne (ed.), Liber Pontificalis, I, 159; De Rossi, Roma sotterranea, II (Rome, 1867), 70-72.