According to the Russian president, this is a military operation to "protect" the population of the two Russian-controlled breakaway regions in eastern Ukraine.
This was just hours after the separatists there asked for Russian military help against alleged attacks from Ukraine, something that is rejected as propaganda by, among others, the United States.
After the speech - several explosions
During the night, several explosions were heard around Ukraine, including outside the capital Kiev.
Gunfire must also have been heard near the capital's airport.
"It sounds like artillery fire, but it could be an air strike," Andrew Simmons, a reporter for al-Jazeera, told the newspaper.
At 05.30 it was still unclear how extensive the Russian operation is.
The Russian military says it has attacked Ukrainian air bases and "other military assets" during the night and morning, Reuters reports.
The Russian state-controlled news agency RIA claims in its reporting that the country's military has struck with high-precision weapons.
At the same time, Russia's Foreign Ministry claims that it is not attacking Ukrainian cities with either robots or airstrikes.
Biden: Unprovoked attack
During the night, Swedish time, US President Joe Biden called Russia's actions an "unprovoked and unjust attack" on Ukraine.
NATO Secretary General Jens Stoltenberg also reacts.
But neither the United States nor NATO will help Ukraine with troops.
They have previously made it clear that they will only protect the territory of NATO countries.
- We are behind Ukraine in this terrible time, says Jens Stoltenberg.
The text is updated