He entered St. Mary's College in Lebanon (Kentucky) in 1821, taught mathematics there at the age of 14, took his degrees in 1826, and studied philosophy and theology at the Bardstown Seminary. In 1830 he entered the College of Propaganda Fide in Rome, where he earned a doctorate in theology by publicly defending 256 theses. Ordained priest in 1834, he returned to Bardstown as parish priest of the cathedral and editor of the Catholic Advocate, founded in 1835. He served as vicar general in Louisville (1844), coadjutor with right of succession (1848), and bishop (1850) of Louisville. There he consecrated the cathedral (1852) and established schools for boys; at Louvain he opened the American College (1857); and he fought through lectures and writings against the Know-Nothing Movement and the then-current system of secular schooling. He succeeded Archbishop Kenrick in the see of Baltimore (1864), presided over the Second Plenary Council (1866), which approved his plan to found a Catholic university. He took part in the centennial observances of the martyrdom of St. Peter in Rome (1867). In 1871 he invited the future Cardinal Herbert Vaughan to evangelize African Americans and assisted Father Hecker in founding the Catholic Publication Society in New York. At the Vatican Council he served on the Commission for Faith and the Commission for Petitions. A firm supporter of papal infallibility, he drafted a memorandum favoring an implicit definition of the dogma rather than an explicit one. Immediately after the definition of the dogma, he issued a pastoral letter to his archdiocese to explain its meaning.
Notable among his apologetic works are Evidences of Catholicity (a series of lectures delivered from 1844 to 1848) and History of the Reformation (1840).