Weaving is the art of creating textiles by interlacing yarn threads at right angles; longitudinal threads in a weave are known as the warp while the lateral threads are known as either the weft or the filling. Most textiles will fall into three categories of weaving: plain weave, satin weave or twill.
We have evidence of the practice of weaving as far back as 27,000 years ago at the Dolní Věstonice Upper Paleolithic archeological site in what is today the Czech Republic, where people were apparently making both baskets and cloth. In the Americas, the oldest found textiles were certainly woven - plant fibre based creations found in Guitarrero Cave, Peru and dated to between 10100 and 9080 BCE.
Modern weaving has most of its origins in the Inca empire, who were using what we would today think of as backstrap looms to produce ceremonial textiles on an industrial scale; when the Conquistadors from Spain came to raid South America, they were impressed by the quality of the cloth and cordage the Incas produced and took a significant quantity back home. When Sicily was later captured by the Normans, they took the weaving technology developed in Spain as a result of the conquest of the Incas over to Northern Italy, where it would spread throughout the rest of Europe.
During the industrial revolution, powered looms invented by Edmund Cartwright transformed weaving from an artisan craft to a humming business; Jacquard looms invented in France would later allow for loom woven textiles to display even the most complex patterns developed by hand weavers, meaning that automation could handle the creation of even very elegant cloth. Today, powered looms coupled with computer interfaces are an integral part of the weaving industry.
We've come a long way from those of us who were weaving baskets in the Upper Paleolithic, but we still use fundamentally the same techniques and we wouldn't have arrived quite where we are without them leading the way.