Unfinished paintings are enticing cracks in the facade of art history, lures along the path to a deeper understanding of artistic processes and impulses. For all the paintings that artists complete, countless others are left incomplete for any number of reasons — poverty or war, a change of plan or vision, the illness or death of the artist. While many of these works have been destroyed, and others forgotten, some are now recognized as significant works of art, accorded a special place in history and in an artist’s body of work, in part because they can bring us closer to understanding the mysterious process of painting, and, indeed, to painting’s future. After all, nothing inspires a young artist like a close look at how an earlier one worked.

I started thinking about unfinished canvases on my first, euphoric visit to the Metropolitan Museum of Art’s reconfigured galleries of European paintings last spring. Everything seemed new, even paintings I had seen scores of times. That’s how I came to be transfixed by Jean-Baptiste Greuze’s “Aegina Visited by Jupiter,” specifically by a striking mass of loose, brushy gray hovering above the reclining, mostly nude form, a cloud that would have done Monet proud. I consulted the label, which explained that that portion of the painting was unfinished.

After rediscovering the Greuze, I came upon three or four more paintings in quick succession whose less-than-complete surfaces were confirmed by their labels as unfinished. A roundup of the Met’s unfinished paintings began to present itself. When I returned to this subject late last fall, the Met provided a list of paintings on view that are considered unfinished. It included more than two dozen works from the 15th century to the late 19th. And a wonderful list it is, full of anomalies and gems. Many of them are discussed here, interspersed with glances at other paintings whose loosening brushwork can sometimes look unfinished but isn’t.

The earliest unfinished European painting on display at the Met right now, in Gallery 640, is a real knockout: “Virgin and Child With Saints” by a Flemish artist referred to as the Ghent Painter (who might be Hugo van der Goes or Jean Hey). This exquisite oil-on-wood image demonstrates one of the stranger ways that a work can be, or in this case become, unfinished. Completed around 1472 in the meticulously realist style perfected by Jan van Eyck (1390-1441), the painting was modified in the early 17th century to depict the marriage of Henry VII to Elizabeth of York. The Virgin and Child in the center and St. John the Baptist to the left of them were scraped off and replaced, respectively, with a central view into a cathedral and the bride. The lavishly dressed St. Louis (himself a king) on the far right became Henry with a few adjustments in crown and gown.