There's actually a Slate article covering this topic[0]. First, consent was given for certain homes. However, the article also notes that under "exigent circumstances" warrantless searches are permitted:

> In exigent circumstances, or emergency situations, police can conduct warrantless searches to protect public safety. This exception to the Fourth Amendment’s probable cause requirement normally addresses situations of “hot pursuit,” in which an escaping suspect is tracked to a private home. But it might also apply to the events unfolding in Boston if further harm or injury might be supposed to occur in the time it takes to secure a warrant. A bomber believed to be armed and planning more violence would almost certainly meet such prerequisites.

[0]: https://slate.com/news-and-politics/2013/04/boston-bomber-ma...

> After the Boston Marathon bombing, they searched a 20-block area for the suspect (and found him). Was that legal?

Uh, why wouldn't a cop be allowed to walk/drive/fly-over public roadways in a 20-block area and look from public land in any direction?

Also do note, they knew specifically who they were looking for and had location data from their cellphones [1]. Not a judge, but if I was and somebody wanted a search warrant to find a person at a location and their evidence was the dude's cellphone is there, I'd grant it.

[1]: https://en.wikipedia.org/wiki/Dzhokhar_Tsarnaev#Manhunt_and_...

Wasn't it a voluntary search?

A resident found him in his boat in his back yard and called police.