Ukraine's air force said Russia had launched 74 missiles and 496 drones overnight, mainly targeting the capital.
While the country's air defences were able to repel most of these, 25 ballistics missiles and 12 drones struck 33 locations.
The BBC team in Kyiv heard loud explosions through the night. By 3:30 local time, we had counted 10 significant strikes, with one major fire in the city centre and multiple other blazes in the distance spotted.
Tracer fire from air defence systems kept lighting up the sky, followed by explosions.
On Thursday morning, daylight brought clearer images of a crater which appeared to be caused by the impact of explosions.
Smouldering cars, buildings and infrastructure could also be seen next to bombed-out debris.
Multiple fires broke out across the city and damage was reported at an ambulance station in the city, which left at least one person critically injured.
Firefighters were also dousing a blaze destroying a hotel on a central boulevard.
The country's state emergency service said 13 people have been killed and more than 30 others injured.
So far 34 people have been rescued, officials said, and rescue operations are ongoing at sites that have been hit, including in a high-rise apartment building and homes in the south-east of Kyiv.
Foreign Minister Andriy Sybiha has called on Ukraine's partners to send more air defence systems, saying the country needed "not only words of condemnation but concrete action to stop Russian terror".
He posted on X that Russia had targeted residential buildings and civilian infrastructure, and called on partners to increasing sanctions on Russia.
Ukraine's US ambassador Olha Stefanishyna wrote in a post on X: "Another horrific night for the residents of the city, who were forced to spend it in shelters."
"Fires and the destruction of civilian infrastructure and residential buildings in several districts of the city."
It marks the first large-scale missile and drone strike by Russia on Ukraine in more than two weeks.
