A search is permissible without a warrant or even probable cause if there is voluntary consent.
Voluntariness is assessed under the totality of the circumstances. Police cannot coerce a suspect to give consent; it must be an intentional relinquishment or abandonment. It is not necessary to prove that the suspect knew of his ability to refuse to consent.
Consent can be withdrawn at any time.
Other people at a residence can give consent to a search as long as police reasonably believe that the person has authority to give consent for the location. However, if any resident expresses a refusal, this trumps any consent given. However, police can come back after a non-consenting resident leaves and get valid consent to search from the consenting resident.