Ukraine's military confirmed on Sunday that the eastern city of Lysychansk had fallen to Russian forces.
"After heavy fighting for Lysychansk, the defence forces of Ukraine were forced to withdraw from their occupied positions and lines," the army general staff said.
Earlier Russia's Defence Minister Sergei Shoigu said his forces had captured Lysychansk and taken full control of Luhansk region.
Ukraine's troops were outgunned there. It had been their last stronghold in Luhansk.
Its general staff said that "to preserve the lives of Ukrainian defenders, a decision was made to withdraw".
Russia has made it clear that controlling Donbas - the industrial region embracing Luhansk and Donetsk - is a strategic priority.
Russia accuses Ukraine of attacking border city
Explosions rocked the Russian city of Belgorod early on Sunday, 40km (25 miles) from Ukraine's northern border.
The Russian defence ministry said air defences had shot down three Ukrainian missiles, but debris had fallen on an apartment block.
The city's governor said four people had died and dozens of residential buildings had been hit. The BBC was unable to verify the impact or cause of the Belgorod blasts.
The ministry called it a deliberate attempt by Ukrainian forces to target civilians - a claim dismissed by Ukrainian officials, who said the Russians had lied about similar incidents in the past.
Russia dredges up landing ship hit by Ukraine
Earlier Russia said it had salvaged a large landing ship, the Saratov, scuttled by its crew after a Ukrainian missile strike damaged it in the port of Berdyansk on 24 March.
A Russian-appointed official, Vladimir Rogov, said Tochka-U ballistic missiles had targeted the Russian-held port. The crew sank the ship "to prevent detonation of the on-board munitions by the fire that had started", he said.
At the time Ukraine said it had hit a landing ship called Orsk in Berdyansk.
Russia's Black Sea Fleet had six landing ships - used to transport tanks, other vehicles and marines - before the war started.
Teachers swap classrooms for trenches
Service in the Ukrainian armed forces has not stopped school teachers and university lecturers continuing their lessons online - sometimes from the trenches.
The BBC's Sophie Williams in Kyiv spoke to the educators and some of their students. They consider it part of their patriotic duty to continue the learning process.
One professor conducts twice-weekly classes on topics such as tourism and sociology from the trenches on his phone.
And a professor of trauma medicine, now working at Zaporizhzhia military hospital, lets his students watch him conduct operations online.