Yes, presidential elections - the official title of the mayor is President in Kraków and other cities in Poland. Today, there are local and regional elections across Poland.
Opinion polls predict that the current mayor, prof. Jacek Majchrowski, will win the elections again, but will not receive a majority of the votes. That means that there will be a run-off election on Sunday, November 4. During Steemfest 3, you may still see election posters around the city, and if you arrive a week early, you could witness campaign rallies or a victory party.
An average of two polls from the past week indicates that 40% would vote for Majchrowski, 30% for MP Małgorzata Wassermann, and 16% for businessman Łukasz Gibała.
Jacek Majchrowski has been mayor since 2002. He used to be a history professor at Jagiellonian University. He's a social-democrat, and he used to be a member of the communist party until 1981, but he has run as an independent candidate since he was first elected. Today, he's supported by the Democratic Left Alliance as well as the neoliberal Civic Platform (PO) party and other centrists. Throughout Poland, independent incumbent candidates, with or without party support, appear to be more popular than any particular party or coalition.
Majchrowski looks like the typical father-figure you'd expect a mayor to be. And he confirms this impression in this soft-ball interview (in Polish) about the working-class suburb Nowa Huta, established in 1949. He doesn't mention that it was created for ideological reasons. A giant steel mill was built in order to move proletarians to the politically unreliable middle-class city. The mayor is promising to renovate 70 streets in Nowa Huta for its 70th anniversary, and if I understand correctly, he registered there as a candidate instead of the district where he lives.
The most serious objection from other candidates seems to be that infrastructure didn't keep up with the rapid economic growth, while air pollution has been neglected. Coal-burning stoves add soot to car exhaust fumes and industrial pollution, creating heavy smog in the Wisła valley when there's no wind in winter.
Małgorzata Wassermann is the candidate from the conservative Law and Justice party (PiS), which runs the national government. She's one of two or three female candidates that has a chance to win in a major city. It would be a dramatic surprise if she could win in such a progressive city as Kraków.
As a member of the Sejm (lower house of parliament), she became popular for leading the investigation into the Amber Gold pyramid scheme. She's the daughter of politician Zbigniew Wassermann, who died in the Smolensk air disaster in 2010, after taking the place of current party leader Jarosław Kaczyński at the last moment.
In Western Europe, PiS is known as a nationalist and religious party, but you could also say they were elected in 2015 as an anti-austerity party. After neoliberal and social-democratic governments had thrown up their hands for years and said there was no money for social spending, the PiS government gave families a child subsidy and cancelled the plan to raise the retirement age. Wassermann is handing out bread not because voters are hungry, but because one of her slogans is "first bread, then circuses". She's making many promises about improving child care and primary education.
Łukasz Gibała is probably not going to win, but he's a fascinating character. As a smug-looking businessman from a rich family who has been in parliament for a number of centre-right and leftist parties, he says he could spend his days relaxing in the Bahamas, but he prefers to help the city and its citizens as a politician. Gibała has a PhD in logic and calls his movement the Logical Alternative.
Since the two top candidates have been in power during a period of strong economic growth and investment in infrastructure, this business-friendly liberal candidate is calling them out for chopping down trees (tys. drzew = 1000 trees). Another indication that the left-right political spectrum doesn't really apply to Poland.
Read profiles of six candidates in the Krakow Post if you want to know more details.
Reading about the Polish elections in general, it surprised me that PiS, which seems to be a well-organized party supported by religious and state media, never does well in local and regional elections, even when you include rural areas. So the results of today's elections won't tell you much about the popularity of the national government. This Friday, the European Court of Justice ordered the Polish government to suspend politically motivated reforms of the Supreme Court. The first response of the ruling party was muted. They want to stand up for national sovereignty, but they don't want to be seen as planning to leave the European Union. Without the EU, Poland wouldn't have such a booming economy.
Update: the results are in. No surprises, there will indeed be a second round between Majchrowski and Wassermann.
In the future, 
Photo credits:
1: Wielopolski Palace, the City Hall, during Kraków Flag Day. By Szczur97.
2 & 4-7: From the candidates' Twitter accounts.
3: President Majchrowski conducting a ceremony in City Hall. By Franciszek Vetulani.