(CNN) -- On June 2, Mexicans will vote to pick their next president in a historic race that could see a woman take the top job for the first time.

In addition to the presidency, there are more than 20,000 positions to fill and an estimated 70,000 candidates vying for those offices, including 128 senate seats and 500 deputy seats; the mayorship of Mexico City; and governor’s offices in Chiapas, Guanajuato, Jalisco, Morelos, Puebla, Tabasco, Veracruz and Yucatán.

Here’s who is running for president:

Claudia Sheinbaum

The 61-year-old Sheinbaum is a former Mexico City mayor and climate scientist. A longtime political ally of incumbent President Andrés Manuel López Obrador, she was the Mexico City environment secretary from 2000-2006 when he was mayor.

If she wins, Sheinbaum would be not only the first female president in Mexico, but the first president with Jewish heritage, although she rarely speaks publicly about her personal background and has governed as a secular leftist.

Her close alignment with López Obrador has been both a blessing and a curse politically. Sheinbaum has said she’s “not a close copy” of López Obrador – but she also doesn’t shy away from touting the principles they share, even repeating his slogans on the campaign trail.

(López Obrador has repeatedly dismissed whispers that he favors a candidate that he could influence, telling press in February that he would “retire completely” after his term.)

Among her policies, Sheinbaum has promised:

• Continuing Lopez Obrador’s pension for all senior citizens
• Scholarships for more than 12 million students
• Free fertilizers for small farm owners
• On security, she proposed consolidating the National Guard, reform of judiciary, strengthening intelligence and research and coordination with law enforcement authorities.

Xóchitl Gálvez

Backed by an opposition coalition of Mexico’s PRI, PAN and PRD parties, Xóchitl Gálvez is a former senator and previously served as the top official for indigenous affairs under former President Vicente Fox.

The daughter of an indigenous father and a mixed-race mother, the 61-year-old was a businesswoman before entering politics.

For a relative newcomer, Galvez’s entry into the presidential race has gained impressive momentum, experts say.

Her proposals include:

• Continuing Lopez Obrador’s pension for all senior citizens
• A “universal social protection system” of welfare programs for middle and lower classes
• A security approach that would strengthen local and state police
• Galvez has also hinted that that oil-rich Mexico should invest more in renewable energy, saying earlier this year: “We haven’t done it because we are dumbasses.”

Jorge Álvarez Máynez

A late entrant in the race, Jorge Álvarez Máynez shot to international attention earlier this month, when a stage collapsed at his campaign event in the northeastern city of San Pedro Garza García, killing nine people and leaving at least 121 people injured.

The 38-year-old has pledged to:

• Eliminate the crime of simple drug possession to to stop criminalizing poverty, and move from prohibitionism to regulation of drugs
• End the longstanding militarization of Mexico and instead focus on training and strengthening police
• He has also proposed a gradual economic reform including a universal pension system, guaranteed labor rights and income and progressive tax reform
• Máynez has also called for transforming the Federal Electricity Commission (CFE) and Pemex into renewable and clean energy companies, and for closing some refineries

The key issues: Security and migration

Security and immigration are top issues for all of Mexico’s presidential candidates.

Campaigning in the run-up to the election has been marred by dozens of assassination attempts and other political violence. There are concerns now that that the attacks have already cooled off campaigns; experts and political parties say some candidates have renounced their bids in fear of their lives.

But electoral violence is just a part of Mexico’s broader security crisis, with sky-high crime and homicide rates. In the first four and a half years of López Obrador’s government, 160,594 homicides were recorded – a figure surpassing that of the previous administration.

However, a report from the Mexican Peace Index (MPI), prepared by the Institute for Economy and Peace (IEP), has offered some reason for optimism, reporting improvements in five key indicators: homicides, crimes with violence, fear of violence, crimes committed with firearms, and crimes of violence. Homicides and crimes committed with firearms peaked in 2019, according to the May 2024 report, and have since improved.

Meanwhile, pressure is growing on Mexico’s southern and northern borders.

In 2023, the National Migration Institute (INM) recorded a 77% increase in migrant arrivals compared to 2022. And as it grapples with the surge of migrants and asylum seekers entering and crossing its own territory, Mexico will also have to contend with external policies on migration.

As an example, Myriam Guadalupe Castro Yáñez, an academic at the National School of Social Work of the National Autonomous University of Mexico (UNAM), points to a recent state law in Texas that has already caused waves in Mexico.

In December, Texas Gov. Greg Abbott signed a bill that would allow state officials to detain and deport people suspected of having entered the United States illegally. The law is currently blocked in a US federal court, but the López Obrador government has warned that it will not receive people deported by Texas and that it will only discuss immigration issues with Washington.

Both Sheinbaum and Gálvez have stated their support for this stance.

Reporting contributed by CNN’s Rafael Romo and David Shortell.

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