The Mary of popular Catholic and Orthodox devotion is met less through doctrine than through apparition, image and title, and the scale of that devotion far exceeds what is formally defined.
Reports of Marian apparitions run through the whole history of the church, but a handful anchor the modern forms: Guadalupe in Mexico (1531), whose image made her patroness of the Americas and a national symbol; Lourdes in France (1858), now a vast pilgrimage of the sick; and Fatima in Portugal (1917), which gathered a following and a set of associated prophecies. Their status is worth stating precisely: the Catholic Church investigates such events and may declare one "worthy of belief", which permits devotion but binds no one to it, apparitions are private revelation, not articles of faith.
The countless titles, Our Lady of Sorrows, Star of the Sea, Queen of Heaven, and hundreds of local Madonnas, attach devotion to particular places and needs, and the rosary structures much of it. Behind all of it lies a distinction the tradition insists on and outsiders often miss: Mary is venerated, not worshipped. Catholic theology reserves adoration (latria) for God alone, calls the honour due the saints dulia, and gives Mary a higher veneration, hyperdulia, as the greatest of them, but not worship. The Second Vatican Council's Lumen Gentium set her firmly within the church rather than above it.
Most Protestant traditions, holding that such devotion obscures Christ, keep their distance, which is why the figure so central to some Christians is nearly absent from others.