More than four months into his term, how close is President Donald Trump to making good on his signature promise to build a wall between the United States and Mexico?

Let's take a look.

Has construction begun?

Doesn't look like it. On his fifth day in office, Trump ordered construction of the wall to begin using cash on hand. ProPublica reported last month that Customs and Border Protection (CBP) had just $20 million in their coffers for the project, which isn't much when cost estimates for building a border wall range from $1 million to $21.6 million per mile.

White House Press Secretary Sean Spicer discusses the building of a proposed border wall at the White House on May 3, 2017 in Washington. Jonathan Ernst / Reuters file

The border between the United States and Mexico is more than 1,900 miles, and there's already 694 miles of existing fence. CBP did not respond to inquiries about whether any stretch of new wall has been built, although there are no signs of any activity. Repairs to 40 miles of older fencing were approved in the 2017 funding bill passed earlier this month, but funds for the concrete barrier that so energized Trump's voters have yet to materialize.

In March, CBP put out a call for proposals that asked for two different design options: the very solid, concrete type that Trump described on the trail, and the alternative-material, see-through wall favored by border experts. Finalists will be announced in June, and prototypes will be built shortly afterward.

For the project to truly get off the ground, Trump needs to convince either Mexico or Congress to give him the cash. Few lawmakers in either party have said that funding for the wall is a priority.

Is Mexico paying for the wall?

During the campaign, Trump promised that Mexico would fund it up front. Now, the president says Mexico will eventually pay for the wall, so any money Congress allocates is just a temporary expenditure.

But Mexico says nope.

"Mexico, of course, will not pay," Mexican President Enrique Peña Nieto said in January, reiterating what he has said repeatedly for the last two years, including to Trump directly during a campaign trail visit.

A U.S. worker inspects a section of the U.S.- Mexico border wall at Sunland Park, U.S. opposite the Mexican border city of Ciudad Juarez, Mexico. Jose Luis Gonzalez / Reuters file

The president insists the U.S. can force Mexico to pay, perhaps by taxing remittances — cash residents send from America to friends or relatives in Mexico. One Republican representative has suggested taxing all transfers between America and Latin countries, NPR reported.

The Border Wall Funding Act of 2017, introduced on March 30 by Alabama Republican Rep. Mike Rogers, would put a 2 percent tax on all person-to-person wire transfers to Mexico, the rest of Latin America and the Caribbean. Remittances are a big deal; $28.5 billion flows into Mexico every year in remittances.

So, who is really going to pay for the wall?

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Taxpayers are expected to pick up the initial tab and, barring a reversal from Mexico or a remittance tax, likely in the long run, too.

How much will it cost?

No one knows for sure, in part because the CBP has yet to chose a design. The Department of Homeland Security reportedly has estimated a wall would cost about $21.6 billion, not including maintenance, while Republican leader Mitch McConnell recently estimated it would cost up to $15 billion. Senate Democrats released a report last month estimating that it would cost about $70 billion to build, and $150 million a year to maintain.

Federal records show that existing fencing built a decade ago cost between $1 million and $3.9 million per mile, with the costs widely varying due to terrain and fencing type. The president’s 2018 budget proposal asks Congress for around $21.6 million per mile to build 74 miles of his wall.

This undated rendering provided by DarkPulse Technologies Inc. shows a proposed border wall between Mexico and the U.S. The wall proposed by the Arizona-based company would be constructed with ballistic concrete that can withstand tampering or attacks of any kind, according to founder Dennis O'Leary. "You could fire a tank round at it and it will take the impact," he told The Associated Press. AP file

What will the wall look like?

Trump promised voters “a big, beautiful wall." But it might not look like a wall at all. It might look more like the 694 miles of fencing already built.

The CBP proposal requirements indicated that the wall would have to be at least 18 feet high and able to withstand significantly physical force, prevent climbing and tunneling and be aesthetically appealing on the American side.

The Wall Street Journal obtained a slew of the sketches, including one Parthenon-inspired design as well as a double-wire mesh fence design that would offer Americans, but not Mexicans, visibility to the other side.

There’s some indication that fencing may indeed rule the day. Touting the funding secured to repair 40 miles of existing border fencing secured in the omnibus-spending bill Congress passed this month, Office of Management and Budget Director Mick Mulvaney showed images of 20-foot cyclone fencing and told reporters this kind of steel fencing might be the "wall" in the end.

“This is the wall that DHS said they wanted, sat in the Oval Office with the president, we talked about bricks and mortar, we talked about concrete, and this is what they wanted,” Mulvaney said, noting that the DHS believes see-through fencing is safer for border agents. “It’s also half of the cost, so we can build twice as much of it.”

Who actually owns the border?

This is where things get messy.

Much of the nearly 2,000 mile-border is owned by private citizens and businesses, whose property will be bought out from under them by the federal government armed with eminent domain laws that can force owners into deals.

“Are people concerned about the federal government coming in and trying to grab their land? Yes, they are.” Texas Rep. Will Hurd told NBC News. The Republican congressman’s district stretches 820 miles along the southern border. “Private property rights are pretty damn important to us.”

The last time the federal government built up fencing along the southern border with the Secure Fence Act of 2006, eminent domain laws were used to buy up a significant amount of land, often at a discount of the land’s value. A CNN investigation reviewed 442 lawsuits involving 678 property owners; the property owners all lost their land, though some cases remain open to this day. In the end, CNN reported, they expect it to cost more than $103 million to the taxpayer for the government to buy up 600 parcels of land and settle unresolved transactions and litigation expenses.

The Trump administration is revving up for a similar fight. The Department of Justice requested $1.8 million for 2018, enough to staff 20 positions, including 12 attorneys, “to meet litigation, acquisition, and appraisal demands during the construction along the border.” The department currently has just two attorneys and a budget of $329,000 for dealing with eminent domain issues.

What about eminent domain?

“I think eminent domain is wonderful,” Trump told Fox News in 2015, breaking with much of his party, who see it as government abusing its power.

As a businessman, he infamously used it to try and force an elderly widow to sell her property so he could build a parking lot for limousines. He lost the case.

Will a wall deter illegal immigration?

That’s the multi-billion-dollar question.

“Walls work, just ask Israel,” the president said last week at a joint presser with the Colombian president, in his most recent public remarks about his signature promise to America. Theadministration is quick to note that illegal border crossings are down significantly this year. DHS Secretary John Kelly credited this last month to "confusion" about how the new administration will handle immigrants, and the president's tough rhetoric on enforcing immigration laws.

Critics say it's a really expensive way to secure the border, which could be more cheaply done with technology, border agents and fencing.

“My goal is that when we look at border security, we do not have a one size fits all solution, we look at every mile of the border differently than we looked at the one before it,” Hurd said.

Existing fencing has not, so far, stopped immigrants from crossing the border. Existing fencing was breached 9,200 times between 2010 and 2015. The government itself says it has yet determine a way of measuring how effective segments of the border walls are at slowing or stopping illegal crossings.

(CORRECTION: May 30, 2017, 9:50 a.m.) An earlier version of this article misstated the cost and composition of the proposed border wall. The per-mile cost of the wall ranges from $1 million to $21.6 million for a barrier that includes fending, non-concrete barriers and concrete, not just for concrete.