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As long as the police have good reason (called "probable cause") to believe that a crime has been committed and that the person they want to arrest committed the crime, they can, with just one exception, make an arrest without asking a judge for a warrant.
The exception? There are few places where the adage "a man's home is his castle" still applies, and an arrest at home is one of them. The police must have a warrant to arrest a person at home if the arrest is for a nonserious offense -- such as a simple assault -- and there is no fear that the person they want to arrest will destroy evidence or cause harm to the public.
To learn more about when search warrants required, read Nolo's article Search Warrants: What They Are and When They're Necessary.