But there's still no clear winner among Democrats after what Sen. Bernie Sanders calls "a virtual tie" with Hillary Clinton.
Speaking late Monday, Clinton said the results still coming in gave her "a big sigh of relief." Clinton also said she was thankful to supporters and looked forward to a contest of ideas against Bernie Sanders. The race will now feature just two candidates. Former Maryland Gov. Martin O'Malley suspended his campaign after failing to gain traction.
Sanders rode a wave of enthusiasm. Polling shows most Democrats favor a continuation of Obama administration policies. But among younger people, Sanders was the overwhelming favorite.
Cruz said his win "sent notice" that the establishment and media won't pick the Republican nominee.
Donald Trump vowed to fight on and said he was "honored" by Iowans. He finished just ahead of Florida Sen. Marco Rubio. He called his performance an important first step.
Cruz's victory in the Iowa caucuses means he'll collect eight delegates to the Republican National Convention.
Ted Cruz' Iowa victory was propelled by Republican caucus-goers who said they want a candidate who shares their values.
That's according to entrance poll interviews of those arriving at presidential caucus sites on Monday night.
Two-thirds of caucus-goers were born-again Christians, and Cruz was favored over billionaire businessman Donald Trump and Florida Sen. Marco Rubio among that group.
More than 4 in 10 Republican caucus-goers said the candidate quality that mattered most to their vote was that the candidate shares their values.
Among those who said so Cruz on the support of more than 3 in 10, versus just 2 in 10 for Trump or Rubio.
The survey was conducted by Edison Research for The Associated Press and television networks.