Russian President Vladimir Putin has praised the sacrifices of the Soviet people in World War Two, addressing the armed forces in Moscow.
The giant, annual Victory Day parade for the first time included missiles adapted for Arctic warfare.
Russia is developing new Arctic bases.
"No force will be able to dominate our people," Mr Putin said, deploring the havoc that Nazi Germany wreaked in the war. The USSR lost more than 20 million people - more than any other country.
The Soviet Union (USSR) ceased to exist in 1991.
Ukraine's President Petro Poroshenko took part in a wreath-laying ceremony in Kiev. He told Ukrainian soldiers that Russia was trying to use the victory anniversary "to satisfy its own revanchist, imperialist and expansionist needs".
"The Kremlin is still trying to command Ukraine as if it commanded the four Ukrainian fronts in the 1940s."
Russia has often been accused of downplaying the role of other nations in the defeat of Nazi Germany.
Western sanctions were imposed on Russia after it annexed Ukraine's Crimea peninsula in 2014. They were ratcheted up - targeting many close associates of Mr Putin - when the Russian military bolstered pro-Russian rebels in eastern Ukraine.
The Kremlin denies helping the rebels militarily, but admits that Russian "volunteers" have joined their ranks.
Military youth movement
The military hardware on show in Red Square on Tuesday included Pantsir-SA air defence missiles in grey-white Arctic camouflage.
Yars RS-24 intercontinental ballistic missiles, which can deliver nuclear warheads, also trundled past the assembled military top brass, government officials and bemedalled war veterans.
Members of a new "military-patriotic" youth movement, called Yunarmiya, participated in the parade for the first time.
The main event was in Moscow, but parades also took place in cities across Russia, many of which were devastated in the 1941-1945 bloodbath that Russians call the "Great Patriotic War".
"To fight terrorism, extremism and neo-Nazism we need the co-operation of the entire world community," Mr Putin said in his short speech.
Russia has deployed many of its latest weapons in the Syrian war, backing President Bashar al-Assad's forces, who are also heavily assisted by Iran.