1) What can police legally search for?

• Under the fourth amendment to the U.S Constitution police are allowed to engage in “reasonable” searches
• For a search to be deemed “reasonable”, law enforcement must have reason to believe that evidence of a crime will be found there
• Police are allowed to do a “protective sweep” for their own safety
• Police may expand their search beyond the warrant’s specifications if there is obvious unrelated evidence
• Police may search without a warrant in “exigent circumstances”, with the person’s consent, or if the person isn’t in an area with a “reasonable expectation of privacy”

2) What can't police do?

• Police require a warrant for searches unless there is consent, exigent circumstances, etc.
• Police may not use evidence that they got from illegal searches against you in a trial
• Police may not use evidence they got from illegal searches to find more evidence

Sources:

Each of the sources below are linked.

From FindLaw "Police Search and Seizure Limitations"