How the Kremlin fares
Gubernatorial elections will take place in 16 regions. Elections to legislative assemblies will take place in 13 regions including Crimea, which Russia annexed from Ukraine in 2014.
Russian voters, battling rising poverty under Western sanctions and a controversial pension reform, have been increasingly willing to punish representatives of the ruling party United Russia.
Many Kremlin-friendly candidates are disguising themselves as independents in a bid to distance themselves from the party, whose brand is now widely seen as a liability.
Six of 16 candidates running for election or re-election as governors have campaigned as independents.
Political analysts say the elections will be a key test of the authorities' ability to stage-manage polls after a major slump in the approval ratings of President Vladimir Putin and United Russia.
Observers do not rule out that members of the ruling party will not be able to win gubernatorial elections in the first round in some regions.
Last year, the Kremlin suffered election blows in four regions where candidates backed by the United Russia ruling party failed to win in the first round.
In the Far Eastern region of Primorsky Krai, claims of irregularities in favour of a Kremlin-backed candidate forced officials to hold a rare re-run of the vote in 2018. It was won by the Kremlin candidate.
The Moscow parliamentary election will be a test of top Kremlin critic Alexei Navalny's ability to mobilise the opposition ahead of parliamentary elections in 2021, following a major police crackdown in the summer.
Popular opposition candidates have been barred from running in the Moscow election and Navalny urged Muscovites to support those with the best chance of beating pro-Kremlin candidates - most of them Communists.
Navalny has also urged residents of other cities to vote strategically.
To encourage Russians to follow his lead, Navalny's team has in recent days turned out daily investigations accusing prominent officials of corruption.
Saint Petersburg vote
The unpopular acting governor Alexander Beglov, a long-time acquaintance of Putin, is expected to sail to victory in the absence of meaningful competition.
But the extent of his victory remains unclear and opposition has claimed that authorities are preparing to rig the vote in Russia's second city.
Opposition newspaper Novaya Gazeta reported this week that some election officials in Putin's hometown had been trained to enter fraudulent votes into ballot boxes "at the last minute".
"Every other vote for A goes to B," Novaya Gazeta quoted a trainer as saying.
Beglov's strongest competitor, the Soviet-era director and Communist lawmaker Vladimir Bortko, suddenly quit the race a week before the vote.
The Far Eastern region of Khabarovsk is where United Russia has fought one of its most bruising campaigns this year.
The region on the border with China will see elections to the regional parliament, the city legislatures and a mayoral vote.
Khabarovsk governor Sergei Furgal of the nationalist LDPR party came to power in a high-profile win last year, securing 70 percent of the vote against incumbent Vyacheslav Shport.
Furgal, 49, has become a popular regional leader, publicly dressing down bureaucrats and amassing 161,000 followers on Instagram.
Many local residents are prepared to support the LDPR which they now associate with Furgal rather than its longtime controversial firebrand leader Vladimir Zhirinovsky.
Following Furgal's victory last year United Russia became the de facto opposition party in the region.