Russia is staging its biggest military parade, marking 70 years of victory over Nazi Germany in World War Two.
Thousands of troops are marching on Red Square in Moscow, and new armour being displayed for the first time.
More than 20 heads of states are in Moscow, but many world leaders are boycotting the event because of Russia's role in the Ukraine crisis.
As the event began, President Vladimir Putin said international co-operation had been put at risk in recent years.
Russia denies claims by the West that it is arming rebels in eastern Ukraine. More than 6,000 people have been killed since fighting began in April 2014 in Ukraine's Donetsk and Luhansk regions.
Show of strength
In his speech, President Putin paid tribute to the sacrifices of Soviet troops during World War Two. He also thanked "the people of Great Britain, France and the United States for their contribution to victory".
But he added: "In recent decades the basic principles of international co-operation have been ignored ever more frequently. We see how a military-bloc mentality is gaining momentum."
The remarks echo previous complaints by Mr Putin about what he says are efforts by the US and its Nato allies to encircle Russia militarily.
The victory parade started at 10:00 local time (07:00 GMT). Chinese President Xi Jinping, President Pranab Mukherjee of India and UN Secretary General Ban Ki-moon are among more than 20 world leaders watching the event.
Military units from across Russia - some dressed in WWII-era uniforms - are marching, and more than 100 aircraft have been flying over Red Square.
The most talked-about new high-tech Russian armour is the T-14 Armata battle tank, which has a remote-controlled gun turret and reinforced capsule for the crew.
The RS-24 Yars intercontinental ballistic missiles - each capable of delivering three nuclear warheads - are also on show.
Russia's Great Patriotic War 1941-1945
- 22 June 1941: Nazi German troops invade Soviet Union, despite 1939 non-aggression pact
- Winter of 1942-43: German advance blocked at Stalingrad, south Russia - about two million soldiers and civilians die in long battle
- 1944: Soviet offensive spreads across Eastern Europe as German troops retreat
- 21 April 1945: Soviet troops enter Berlin
- 30 April 1945: Hitler commits suicide
- More than 60 million war dead globally - heaviest losses were Soviet, an estimated 26 million
In a sign of closer ties between President Vladimir Putin's Russia and China, a column of Chinese troops are marching in Moscow for the first time.
Military parades on a smaller scale are also being held in other cities, including Sevastopol in Crimea - Ukraine's southern peninsula annexed by Russia in March 2014.
'Parade of cynicism'
The US, Australia, Canada and most of the EU heads of state are boycotting the celebrations in Russia over its alleged involvement in the Ukraine crisis.
On Friday, Poland organised an alternative event for those leaders who refused to go to Moscow.
Events in Gdansk were attended by the presidents of several countries including Bulgaria, Czech Republic, Estonia, Lithuania, Romania and Ukraine. Mr Ban was also there.
Addressing the gathering, Ukrainian President Petro Poroshenko said: "Crimes are committed today in the 21st Century amid the aggression against my country Ukraine, despite the cruellest lessons of the past."
The Ukrainian leader also described Saturday's event in Moscow as a "parade of cynicism".