Kryvyi Rih is a city in central Ukraine. It hosts the administration of Kryvyi Rih Raion and its subordinate Kryvyi Rih urban hromada in Dnipropetrovsk Oblast. The city is part of the Kryvyi Rih Metropolitan Region. Its population is estimated at 603,904 (2022 estimate), making it the seventh-most populous city in Ukraine and the second largest by area. Kryvyi Rih is claimed to be the longest city in Europe.

Located at the confluence of the Saksahan and Inhulets rivers, Kryvyi Rih was founded as a military staging post in 1775. Urban-industrial growth followed Belgian, French and British investment in the exploitation of the area's rich iron-ore deposits, generally called Kryvbas, in the 1880s. Kryvyi Rih gained city status in 1919.

Stalin-era industrialisation built Kryvorizhstal in 1934, the largest integrated metallurgical works in the Soviet Union. After World War II, Kryvyi Rih experienced renewed growth through to the 1970s. The economic dislocation associated with the break-up of the Soviet Union contributed to high unemployment and a large-scale exodus from the city in the 1990s. The privatization of Kryvorizhstal in 2005 was followed by increased foreign and private investment which helped finance urban regeneration. Beginning in 2017, there were major labour protests and strikes.

Since the beginning of the Russian invasion of Ukraine in February 2022, Kryvyi Rih has been the target of frequent Russian missile strikes. It was a focus of the southern Ukraine campaign, but the closest ground advance by Russia stalled some 50 kilometres (31 mi) to the south of the city before it was turned back in March 2022.

Kryvyi Rih, which in Ukrainian literally means 'crooked horn' or 'curved cape', was the name originally given in the 18th century to the general area of the present city by Zaporozhian Cossacks. According to local legend, the first village in the area was founded by a "crooked" (Ukrainian slang for 'one-eyed') Cossack named Rih (literally, 'horn'). The name likely derives from the shape of the landmass formed by the confluence of the river Saksahan with the Inhulets.

In 1734 the Cossack Zaporozhian Sich (or Host) incorporated the area within the Inhul Palanka division of their de-facto republic. A list of villages and winter camps (zymivnyky) from that time mentions Kryvyi Rih. In 1770, Kryvyi Rih was again recorded as the camp of the Zaporozhian Sich.

In May 1775, after the end of the Russian-Turkish War, Russian authorities established Kryvyi Rih as a staging post, in the tradition of the Mongol yam, on the roads to the Russian garrisons of Kremenchuk, Kinburn foreland and Ochakov. In August 1775, on the direct order of Catherine the Great, the Sich was forcibly dissolved. The Cossack lands were annexed to the Russian province of Novorossiya and distributed among the Russian and Ukrainian gentry.

The early 19th century saw the construction of the first stone houses (1828), and three water mills. In 1860, the village was designated a township.