Here are five things to know about the election:
1. CSU supremacy in Bavaria is in danger
Since 1957, Christian Social Union (CSU) prime ministers have ruled Bavaria. They have only been in opposition once, in 1954, since their founding in 1945, but even then they received 38% of the vote.
In 2008, the CSU lose their absolute majority in parliament, but they regained their seats five years later.
At Bavaria's last state election, the CSU secured 47.7% of the vote. In the state parliament in Munich, 101 of the 180 deputies came from the centre-right party.
But in recent months, the Christian Social Union has crashed spectacularly in the polls.
The CSU is the Bavarian branch of Chancellor Angela Merkel's Christian Democratic Union (CDU). It is solely active in Bavaria, while the CDU operates in Germany's other 15 federal states.
Stretching across 70,000 square kilometers, Bavaria is the largest German state in terms of surface area and, with 13 million inhabitants, is the second most populous below North Rhine-Westphalia.
In recent decades, its population has grown much faster than the German average, mainly due to immigration from other parts of the country. Bavaria boasts a strong economy, has the lowest unemployment rate and pays billions every year into the financial equalisation system which lowers the income gap between rich and poor states.
One explanation for the CSU's increasingly poor outlook is the refugee crisis of 2015, when hundreds of thousands of asylum seekers entered Germany via Bavaria. The rise of the Alternative for Germany (AfD) has since come as a shock for the Christian Socialists, since CSU patriarch Franz Josef Strauss (1915-1988) established that there should be no democratically-legitimised party on their right.
"In recent months, the CSU has managed to alienate liberal voters without luring back voters from the right," writes news magazine Der Spiegel.
After the elections, Bavaria's Prime Minister Markus Soder may need one or more coalition partners to stay in power. If the Free Democratic Party (FDP) succeeds in re-entering parliament, a centre-right alliance of CSU, FDP and Free Voters (independent candidates) would be the most likely option. Otherwise a black-green coalition of CSU and Greens (like the one between CDU and Greens in the state of Hesse or Baden-Wurttemberg) could be conceivable.
2. Is CSU leader Horst Seehofer to blame for the bad polls?
In Bavaria's CSU, many blame Federal Minister of the Interior and CSU leader Horst Seehofer for the bad polls. According to the media, CSU delegates in Berlin back Seehofer, but many other critical voices remain.
His dispute with Angela Merkel over refugee policy in the governing coalition has caused negative headlines for months.
"Should he stay or leave? This is how Seehofer divides the CSU" reads one headline in German daily Augsburger Allgemeine.
The Abendzeitung Munich tabloid quotes a district administrator as saying: "Since the Maassen affair it has become clear that Seehofer is no longer the right man to lead the CSU into the future. If the election turns out as badly as feared, he should face the consequences and [withdraw]".
Seehofer, who wants to stay as chairman of the CSU, said in an interview with daily paper Suddeutsche Zeitung: "In the last six months I have not interfered in Bavarian politics or in election campaign management. That is Soder's personal prerogative. He is responsible for strategic decisions made during the election campaign."
In fact, beyond the Seehofer-Merkel power struggle there is a tussle between Horst Seehofer and his successor as Bavaria's Minister, President Markus Soder.
CDU Secretary General Annegret Kramp-Karrenbauer made it clear Sunday that it would not be acceptable for people to talk publicly about who was to blame for a defeat, even before an election. CDU and CSU must now concentrate on convincing voters in Bavaria and Hesse to back the Union and stop arguing in public.
3. What role does Markus Soder play?
Bavaria's Prime Minister Markus Soder may be responsible for the CSU's worst result in Bavaria.
He took office as state leader in March, replacing Seehofer who had become German interior minister in Merkel’s new cabinet.
Soder, from Nuremberg, has been married to Karin Baumuller-Soder since 1999. With her brother, she runs her family's construction company. The couple has three children. Soder also has a daughter from a previous relationship.
A protestant christian, Soder's decision in April to hang crucifixes in Bavarian state buildings was controversial and even criticised by church representatives.
Soder, like Seehofer, is also a hardliner on refugee issues, and is famous for his carnaval costumes.
4. Why are the Greens on the upswing?
The Greens' top candidate Katharina Schulze once said "people want politicians who solve problems instead of creating problems".
In the polls, the Greens are Bavaria's second strongest party, well ahead of the Social Democratic Party (SPD). Only their co-lead candidate Ludwig Hartmann was invited by Bavarian Broadcaster Bayerischer Rundfunk to a television duel against Markus Soder.
Organic produce is on the rise, people are worried about bee mortality and they miss Christianity in the CSU. All these arguments have their place on the Greens' political agenda.
The economy — including the car and aviation industry — does not suffer when the Greens are in government, as has been demonstrated by authorities in Baden-Wurttemberg and Hesse.
And the black-green coalition? Suddeutsche Zeitung quotes Green politician Anton Hofreiter: "The trenches aren't that deep ... Bavaria is approaching the Greens and our issues as part of a process of mutual discovery".
So 'yes' to an alliance with the CSU?
One could talk to the Greens about humane and ecological policy, "but not about an authoritarian or anti-European policy", he says.
5. Why are there protests in Munich?
Tens of thousands of people marched through Munich this summer against Bavarian refugee policy and harsh rhetoric from CSU politicians under the motto '#ausgehetzt'. In October, another 40,000 people in the Bavarian capital protested against "politics of fear", according to organisers.
The SPD's top candidate, Natascha Kohnen, said people took to the streets "because they have had enough of being pitted against minorities, of having social issues overlooked — important issues that affect everyday life: whether you can afford your apartment, whether you can get a place in a day-care centre."
Despite this, the SPD slipped further and further in the polls and now fights with AfD for third place, closely followed by Free Voters.
Then there have been protests against rent rises. For years, Munich has been the most expensive city in Germany for both tenants and students.