In an online petition, op-eds, and in testimony by one of their leaders to a shadow Congressional hearing organized by Democrats in Washington, the Stoneman Douglas students galvanizing the new teen movement against gun violence have advanced five policy demands. The goals provide the substance of what they will be marching for this Saturday.

The reform objectives of the March for Our Lives organizers encompass policies popular with the public and advanced by many well-established gun violence prevention groups. But in keeping with their dauntless and sometimes confrontational advocacy, they take a notably aggressive tack with some of their proposals. They have not only called for a ban on assault-style rifles like the AR-15, but also for an “extensive buyback” of such weapons, and suggested that Democratic candidates who are not onboard should face a primary.

Here’s what else to know about the Parkland students’ prescriptions for gun safety:

1. Mandating universal background checks

Requiring that every gun buyer undergo a background check — including for transactions between friends, through private sellers at a gun show, and arranged online — has for years been an overwhelmingly popular policy idea. It’s only become more so since Parkland, according to a Quinnipiac poll. The survey found support for universal background checks at 97 percent among both general respondents and members of gun-owning households.

Today, all 10 states with a Democratic governor and at least one Democratic-controlled legislative chamber already have universal or expanded background checks, thanks to the spread of those laws at the state level following the massacre at Sandy Hook Elementary School in 2012. The next frontier for universal background checks, then, is purple states — where Republican legislative gains flowing from the Trump surge of 2016 present obstacles this session. Consider: A bipartisan background check bill in Minnesota that counted an NRA member as one of its sponsors just got stymied by a Republican-controlled state House committee.

2. Banning high-capacity ammunition magazines

Many rampage shootings, and a growing number of gun homicides and assaults in some cities, are carried out with firearms that can fire a dozen or more times before reloading. The more shots an assailant can get off, the greater the general odds of casualties. That’s why experts we’ve interviewed conclude that limiting how many rounds an ammunition magazine can hold, more so than outlawing assault-style rifles, may be more effective in reducing overall gun violence.

Polls conducted after Parkland show that roughly two-thirds of Americans support restricting the size of ammunition magazines, generally defined as those capable of holding 10 or more rounds. But such laws are not currently widespread: Just eight states and the District of Columbia have one.

3. Banning assault-style weapons

Rifles like the AR-15 have been the means of many mass shootings. They’re much more rarely used in everyday gun violence. The Parkland activists, who’ve taken numerous steps to build an inclusive movement, ground their case against assault-style weapons not in terms of a ban’s potential reduction in total shootings, but instead around the question of whether any civilian needs a “weapon of war.”

Florida’s Republican-controlled government rejected a Democratic bid to ban assault-style weapons while passing a slate of gun reforms this month, but a win for gun violence prevention advocates on this issue in that gun-friendly state could break the dam: An internal poll conducted by Republicans in the state Senate showed a majority of Florida gun owners support outlawing the sale of AR-15s and guns like it, and a group of operatives is mounting an effort to place a constitutional ban on the state ballot.

4. Funding federal gun violence research

One estimate holds that research on gun violence is underfunded by more than $1 billion, relative to other common causes of death. The shortfall is commonly attributed to the notorious 1996 Dickey Amendment, which forbade the CDC from funding research that can be seen as promoting gun control. CDC leaders, interpreting the stricture conservatively, have authorized almost no studies of gun violence at all in the ensuing 22 years.

This week, Republicans in Congress agreed to include language clarifying that the CDC is allowed to research the causes and conduct studies of gun violence as part of the omnibus spending bill that lawmakers need to pass in order to keep the government funded. The move followed comments by incoming Health and Human Services Secretary Alex Azar, who signaled his openness to federally fund gun violence research by saying his agency is in the “evidence-generating business.”

But evidence gathering costs real money, and public health researchers we’ve spoken with are nonplussed by the new budget language. They say what will really make a difference is appropriating significant funds to gun violence research by the CDC — and allowing it to flow both to research into the factors driving our country’s elevated rates, and to evaluations that could identify policies and interventions that could bring those rates down.

5. Digitizing gun purchase records, so crime guns are easier to trace

Until two years ago, federally licensed firearms dealers (or FFLs) could not keep digital sales records without first getting permission from the Bureau of Alcohol, Tobacco, Firearms and Explosives. A rule change in April 2016 brought gun retailers into the 21st century. But they’re still not required to maintain digital records. And other hurdles remain: By law, the ATF may not maintain a registry of guns, gun sales, or gun owners, and the scans of gun store records that the ATF creates at its national tracing center must be left “non-searchable”: investigators can pull up the files pertaining to a given store, but then they have to flip through individual documents chronologically until they locate the record they are seeking.

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