Cruz is also in second in South Carolina, also by some distance. But that's better news for him, as we'll explain below.
How has he performed?
Cruz's campaign has been one of the few slow-and-steady efforts of the year. He has done well in fundraising by tapping into his strong network of conservative support, which has let him be patient as he's slowly climbed in the polls.
Two things happened in November that moved him into the upper tier of contention. One was his strong performance in the third Republican debate -- during which he excoriated the moderators, specifically, and the media in general -- which brought him a lot of new attention. Secondly, the terror attacks in Paris, which happened a few days later, drastically undercut support for Ben Carson, who'd been a favorite of the same conservative/evangelical voters for whom Cruz was competing.
That positioned him well for Iowa, which has regularly seen a voter pool that's strongly evangelical and very conservative. Most impressive about his Iowa win, though, was that he came from well behind Donald Trump to do so.
What are his strengths?
...And that's a sign that his campaign organization and ability to turn out votes is substantial. Having broad support is great, but if your people don't vote, it doesn't help. Cruz was able to get his folks out in Iowa, and he won.
More broadly, Cruz can make a strong argument that he's been a consistent advocate of conservative principles during his time on Capitol Hill. Sure, he hasn't been on the Hill long and, sure, his position on the 2013 immigration reform bill requires some verbal gymnastics, but this was the guy who told conservative activists in the summer of 2013 that he was willing to shut down the government over Obamacare -- and then did it.
Cruz's outspoken disdain for members of the Republican elite might be disadvantageous in most elections, but in 2016, when populist anger at the Republican establishment is hitting a new high-water mark, it's a strong place to be.
He's also a good campaigner, who can hold his own on the debate stage or in one-on-one conversations with voters. He's been savvy about locking up as much support from the evangelical movement as possible and deploying well-known conservatives on his behalf in Iowa. And his campaign has one of the most interesting and deliberate strategies for assuring voters get to the polls of any campaign on the Republican side.
What are his weaknesses?
Cruz is a smart guy, but he's not a popular one. The Republican establishment isn't thrilled about the prospect of a President Trump, but a lot of them are much less thrilled about the idea of a President Cruz. So far, that hasn't mattered, but if the field narrows and as more states with less conservative electorates start to vote, the weight of the Republican elite could be brought to bear more directly against Cruz.
His strong support from conservatives -- and his defined position as being anti-compromise and anti-moderate -- plays well in Iowa and less so in New Hampshire. In states with smaller conservative voting blocs but more voters (like Michigan, Illinois or Ohio), he could have some trouble adding big numbers to his delegate totals.
What would it take for him to win the nomination?
It was important that Cruz won Iowa. If there was any state that was squarely in Cruz's wheelhouse, it was Iowa.
He won't do as well in New Hampshire, but that may not matter. There are a slew of Bible Belt states voting not too far down the road, and Cruz will likely do well there, assuming that a poor showing in New Hampshire doesn't send his supporters looking for someone more viable. Should he have skipped New Hampshire and focused on South Carolina? Maybe. But he didn't.
Cruz is fairly well-positioned as an anti-establishment senator -- a guy who pushes back against the things people hate about Washington but who has at least been to Washington. Republicans who are freaked out about Donald Trump may be less freaked out about Ted Cruz, and Republicans who want someone with experience but who will fight for conservative values may end up in the same space.
With his Iowa win, Cruz leads in the delegate hunt. A reasonable showing in New Hampshire and a strong performance in the South in early March would keep Cruz at or near the front of the field. The only question then is: Who's left to compete with him?