Pillement was born in Lyons, where his father was a designer at La Grande Fabrique, the prestigious Royal silk manufactory. He completed his training in Paris at the Gobelins tapestry manufactory, before departing for Madrid in about 1745, the start of an itinerancy that would characterize his entire career. Pillement painted landscapes, genre scenes, chinoiserie designs, and decorations in Spain, Portugal, France, and London, where he exhibited in the 1760s. By 1763 he was drawing-master to the Imperial family in Vienna. In 1767 Stanislaus Augustus Poniatowski (1732–1798), King of Poland, appointed him his personal painter, as Marie Antoinette (1755–1793) would in 1778. Pillement also prepared "One Hundred and Thirty Figures and Ornaments and Some Flowers in the Chinese Style" (1767), a collection of prints of the decorative, genre, and landscape subjects for which he is best known.
A Shipwreck in a Storm typifies the work of Pillement's late years, in Portugal and France, from 1780 onward. The despairing figure with the outstretched arms is the focus of his composition and a stock image from his marine landscapes. Although this pastel has no known pendant, Pillement often painted his marine views (both oils and pastels) in pairs. The first, typically of a seaport, would depict tranquil, benevolent nature; its pendant, by contrast, showed violent storms and shipwrecks. A Shipwreck in a Storm dramatically illustrates the power of nature, evoking sympathy for the human figures caught up in it.