Sihon king of the Amorites captured the area north of the Arnon from the Moabites, who controlled it earlier. Israel then occupied this region for several hundred years. King Mesha of Moab reclaimed it around 830 BC (see 2 Kings 3:4–27). This came through a campaign detailed on the Mesha Inscription (also known as the Moabite Stone).
Heshbon is usually considered to be Tell Hesban. No evidence yet has shown that people lived there in the Late Bronze Age (see study note on Numbers 21:1).