The over-arching Zapad war games run to September 20 and are taking place in Belarus, western Russia and Russia's exclave of Kaliningrad.
Moscow says almost 13,000 Russian and Belarussian service personnel are taking part, as well as around 70 planes and helicopters.
Almost 700 pieces of military hardware are being deployed, including almost 250 tanks, 10 ships and various artillery and rocket systems.
'Purely defensive scenario'
NATO officials say they are watching the "Zapad-2017" ("West-2017") war games with "calm and confidence", but many are unnerved about what they see as Moscow testing its ability to wage war against the West.
Russia says the exercise is rehearsing a purely defensive scenario.
Putin, commander-in-chief of Russia's armed forces, has often appeared at such events in the past, using them to bolster his image among Russians as a robust defender of the country's national interests on the world stage.
Once the paratroopers and their vehicles have landed behind the lines of their simulated enemy, their task will be to wage war against what the defence ministry in a statement called "illegal armed formations" and to destroy their opponents' vital infrastructure and command centres.
President Putin is watching!
President Vladimir Putin arrived at a remote army training ground on Monday to watch a military parachute drop, part of Russia's biggest war games since 2013 that have the West looking on nervously.
The Russian leader, 64, has not yet said whether he will run for what would be a fourth presidential term in March but is widely expected to do so.