The actions could have broad implications for the estimated 11 million undocumented immigrants in the United States and set up a potential showdown between the federal government and cities that resist the enforcement of some federal immigration laws.
Here's what the orders mean:
About That WallThe first order, entitled "Border Security and Immigration Enforcement Improvements," is the first concrete step President Trump has taken to deliver on his campaign promise to build a "big, beautiful wall" along the southern border with Mexico.
"Beginning today, the United States of America gets back control of its borders," Trump said in remarks at the Department of Homeland Security after signing the order Wednesday.
The order defines it as a "physical wall or other similarly ... impassable physical barrier" and calls for the addition of 5,000 border patrol agents.
The order does not specify how the wall would be funded, though the White House continues to insist that Mexico would reimburse the United States for the cost, even though U.S. taxpayers would foot the bill upfront.
The president of Mexico has said that Mexico would not pay.
Republican congressional leaders said today they will move forward with plans to approve funds for a wall they estimate would cost $12 billion to $15 billion, leaving Trump to "deal with his relations with other countries on that issue and others."
One section of the executive order sheds light on how the United States might find the funds to build the wall, instructing the head of government departments and agencies to identify all sources of aid or foreign assistance the United States has given to Mexico in the past five years.
But total U.S. aid to Mexico in 2016 was $161 million, which is only a fraction of the estimated cost.
Trump has estimated the wall could cost $8 billion to $12 billion. He told MSNBC host Tamron Hall last February that he only needed a 1,000-mile wall along the nearly 2,000-mile border. "Of the 2,000, we don't need 2,000, we need 1,000 because we have natural barriers ... and I'm taking it price per square foot and a price per square, you know, per mile," he said of how he arrived at his estimated cost.
However, an analysis published in the MIT Technology Review noted that building a new 1,000-mile wall could cost as much as $40 billion. Their breakdown includes the current price of steel and concrete.
For comparison, the portion of the 700 miles of fencing built in 2007, under the Secure Fence Act of 2006 signed by President Bush, was estimated at about $2.8 million a mile, according to the Congressional Research Service in a 2009 report to Congress. That cost did not include expenses for upkeep.
White House Press Secretary Sean Spicer floated a possible 20 percent border tax on Mexico as one possible idea for paying for the wall today.
"I think when you take a look at the plan that's taking shape now using comprehensive tax reform as a means to tax imports from countries that we have a trade deficit from, like Mexico," he said. "We can do $10 billion a year and easily pay for the wall just through that mechanism alone."
Spicer later clarified that he was just presenting one possible option to pay for the wall and that a broader "comprehensive tax reform" plan is "in the early stages" of being crafted by the White House, with the close cooperation of congressional leaders.
"Our job right now isn't to roll something out or to be prescriptive, it's to show there are ways the wall can be paid for, full stop," Spicer said, qualifying his previous comments.
Trump's order also calls for ending the "catch and release" policy that temporarily releases some undocumented immigrants because of the limited detention space. They are told to appear in immigration court at a later date.
Sanctuary Cities and Domestic EnforcementThe second order, entitled "Enhancing Public Safety in the Interior of the United States," is designed to enhance the enforcement of immigration laws within the United States.
The order calls for prioritizing the deportation of undocumented immigrants who have, among other things, been "convicted of any criminal offense," "have been charged with any criminal offense," "have committed acts that constitute a chargeable criminal offense" or "have engaged in fraud or willful misrepresentation in connection with any official matter."
The language means that all 11 million estimated undocumented immigrants in the United States could potentially be a priority for deportation, on the basis that anyone who came to the country with no border inspection committed a criminal misdemeanor and anyone who overstayed a visa committed fraud, even though it's not a crime, some legal experts told ABC News.
The order gives wide discretion to ICE officers in making such determinations. The language is "remarkably broad" and "takes that notion of 'criminal alien' to its farthest reaches," University of Virginia professor and immigration scholar David Martin says.
Michael Wildes, an immigration attorney who formerly represented Trump Models, the Miss Universe Organization and Melania Trump, told ABC News "this is scary stuff for America's legacy of immigration, for business and for our hospitality."
The order also aims to strip federal grant money from "sanctuary cities," which The Associated Press defines as jurisdictions that do not generally cooperate with federal immigration enforcement.
Such cities are "not eligible to receive Federal grants, except as deemed necessary for law enforcement purposes by the Attorney General or the Secretary," according to the order.
That could be read to bar any federal funds, including law enforcement funds, to these cities, professor Peter Schuck of Yale Law School said.
The order gives the U.S. attorney general and secretary of the Department of Homeland Security the authority to designate what cities constitute sanctuary jurisdictions.
Since Trump signed the order, elected officials in some sanctuary cities across the country have vowed to continue their policy of protecting immigrants.
New York City is among those sanctuary cities promising to fight the order.
"Any attempt to bully local governments into abandoning policies that have proven to keep our cities safe is not only unconstitutional but threatens the safety of our citizens," New York Attorney General Eric Schneiderman said in a statement. "I urge President Trump to revoke this Executive Order right away. If he does not, I will do everything in my power to fight it."
The action also calls for adding 10,000 additional border enforcement officers, effectively tripling the number of Immigration and Customs Enforcement officers.
The order also calls for the creation of an "Office for Victims of Crimes Committed by Removable Aliens" that will be dedicated to helping U.S. citizens who have been victims of crimes by undocumented immigrants.
"We hear you. We see you. You will never ever be ignored again," Trump said, referring to the victims.
The latest available government data, in a 2011 Government Accountability Office report, placed the number of what it called "criminal aliens" in federal prisons in 2010 at around 55,000, or roughly 3 percent of the total prison population of 1.6M prisoners, and found 90 percent of "criminal aliens" sentenced in federal court in 2009 were convicted of immigration and drug-related offenses.
ABC News' Lauren Pearle contributed reporting.