Illegal immigration is a decades-old problem. With an estimated 11.5 million illegal immigrants living, and in many cases working, in the U.S. the question remains: What do we do with them? And how do we stop more people from coming? Lax enforcement potentially leads to more illegal immigrants competing with U.S. citizens for jobs and some social services, without necessarily paying income taxes. But a too-tight policy could mean farmers and others in industries that rely on the cheaper labor of illegal immigrants are left begging for workers, passing higher costs on to consumers or going out of business altogether.

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Where they stand:

President Barack Obama has pushed for the DREAM Act, a path to citizenship for many young illegal immigrants who arrived in the U.S. as children. Efforts to pass the bill have repeatedly failed, most notably in 2010 when it stalled in a Democratic-led Senate after failing to win the 60 votes it needed to proceed to a full vote. Five Democrats voted against the measure. In June, Obama announced a plan to delay deportations for many illegal immigrants who would have benefited from the DREAM Act for up to two years and let them get work permits.

Mitt Romney has said that as president he would veto the DREAM Act should it ever cross his desk. He told The Denver Post that he would honor work permits for those immigrants who benefit from Obama’s new policy and promised to put a comprehensive immigration plan into place before those permits expire. He favors completing a towering steel fence along the Mexican border, in addition to the 650 miles already constructed, and opposes letting illegal immigrant students pay in-state tuition at state universities.

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Why it matters:

Illegal immigration has slowed in recent years, with the Border Patrol recently recording the fewest arrests in almost 40 years. But many people worry that the Mexican border, the most popular crossing point for newly arriving illegal immigrants, still isn’t secure more than a decade after the Sept. 11, 2001, terrorist attacks.

In the last several years, the government has spent billions building a fence, doubling the number of Border Patrol agents and adding a slew of high-tech gadgets to stop the flow of illegal immigrants. The numbers tell a compelling story: In the last budget year, the Border Patrol arrested about 327,000 people at the Mexican border. In 2006, agents made more than 1 million such arrests.

Obama’s administration also deported a record number of people last year, nearly 400,000. The government has been shifting its focus to finding and deporting criminal immigrants and those who otherwise pose a threat to security.

There’s room for debate about what has led to the steep drop in arrests; it’s quite clear the struggling economy has made it less attractive to enter the U.S. Still, Republicans insist any illegal crossings are too many. And there’s broad agreement that the border should be more secure.

As for illegal immigrants already in the country, there’s no easy answer about what to do.

In 1986, under President Ronald Reagan, Congress approved an amnesty that granted millions of immigrants legal status while also changing the law to make it illegal to hire illegal immigrants.

Hiring has continued in many sectors, notably farming. And some lawmakers worry that agriculture would sink if there were an aggressive effort to verify that all farmworkers could legally work in the U.S.

Various overhauls of immigration policy have been proposed since the early 2000s. But the debate often boils down to Republicans wanting the border secure before anything else, and Democrats pushing for that security and for a path to legalization at once. The result has been a legislative stalemate.