Most teams will have at least one or two of those undrafted rookies on their 53-man roster, with some clubs relying on more of them if their past late-round draft picks can't beat them out for roster spots. Here are 20 players that I think have great chances to make their new team.
Note: The undrafted free-agent market is still fluid, and many teams have not yet confirmed their signings. This list is based on reports and official transactions.
The skinny: Frazier has a chance to become a dangerous pass-rush specialist in Seattle's system due to his quickness and length.
The skinny: For an Eagles team needing depth at tackle, finding a big-bodied swing tackle like Weathersby after the draft was a nice bonus.
College: South Florida
The skinny: An undersized but competitive corner, Nichols has a great chance to make the Cardinals, who need help at the position.
The skinny: Jackson's a physical corner who refuses to back down from bigger receivers. He'll earn himself a role right off the bat.
College: Texas Tech
The skinny: Yes, he's an Air Raid quarterback, but Shimonek has the mental acumen to run an NFL offensive effectively, which is an underrated quality of a young backup. He also has the physical ability to move the ball at the next level. I think he has a chance to beat out Geno Smith for a roster spot.
The skinny: While he comes from the Division III ranks, Gono's got the game for the next level. I suspect he'll make the team this year and compete for a starting spot in Year Two, using his size, nasty demeanor, and surprising agility to move from tackle to guard.
College: Penn State
The skinny: I don't care that Haley (5-9) lacks ideal height. He's competitive and quick, making him an excellent nickel defender. That's something the Giants needed to get out of draft weekend.
College: South Carolina
The skinny: Defensive tackle depth is an issue for the Saints, and they did not have enough picks to address it during the draft. But they found a draftable player in Stallworth after the proceedings. He has the size and hustle to make an impact as a rotational player in 2018. He could play an even bigger role down the road.
College: San Diego State
The skinny: The expected retirement of Jason Witten made finding a tight end crucial for Dallas. Drafting Stanford's Dalton Schultz in the fourth round made sense, and Rico Gathers still has potential, but Wells will compete for a roster spot because he can make an impact as a blocker and a receiver.
16) Jalen Davis, CB, Dolphins
College: Utah State
The skinny: Davis should have received a lot more attention through the draft process, but his lack of size was a hurdle for teams. If you flip on the tape, he shows the stuff of a pro cornerback. He'll have an opportunity to compete to become one of Miami's top four corners, and he has a good chance to stick.
The skinny: Depth on the interior offensive line was a need area for Washington, so landing this versatile former Hawkeye after the draft was key. He might line up next to former teammate Brandon Scherff in the pivot in 2018 or 2019.
The skinny: Blanding's lack of top-end speed cost him a draft slot. He will compete for playing time with fourth-round selection Troy Apke, however, because he's a instinctive player and an expert tackler in space.
19) David Steinmetz, OT, Dolphins
The skinny: At 6-8 and 310 pounds, Steinmetz is just plain difficult to get around. He'll get a good chance to make the roster in Miami if he can emulate similarly built Sam Young's game during training camp.
20) De'Mornay Pierson-El, WR, Redskins
The skinny: Washington had one of the worst punt-return averages in the league last season, and Pierson-El excelled in that role at Nebraska. He also had five touchdowns last season as a receiver, so he could back up Jamison Crowder in the short-receiving game, as well.