Pour-over as we know it starts with a woman in Dresden who was tired of grounds in her cup. Melitta Bentz punched holes in a brass cup, lined it with blotting paper from her son's school exercise book, and poured coffee through it. In 1908 the Imperial Patent Office in Berlin registered her coffee filter, and on December 15 that year she and her husband, Hugo, started the business that still carries her name.
In the 1930s the company patented the cone-shaped paper filter, the shape most drippers still use. In 1941 the chemist Peter Schlumbohm, then working in New York, received a U.S. patent for a filter funnel joined to a flask. It became the Chemex, now in the collection of New York's Museum of Modern Art.
The idea hasn't changed: hot water, ground coffee, a paper filter, and a little patience.