Amendment III
"No soldier shall, in time of peace be quartered in any house, without the consent of the owner, nor in time of war, but in a manner to be prescribed by law." (Source)

The third amendment has never had a case brought to the Supreme Court concerning it. This is most likely attributed to the little room for interpretation on our parts. There was one 2nd Circuit Court case, Engblom v. Carey (1982). In this case, the prison guards were on strike (details), the Governor of New York brought in the National Guardsmen. Due to the strike lasting 16 days they Guardsmen were housed in company houses. This was not allowed by the owners, the decision went in favor of the defendants (guardsmen) because they were not knowingly breaking the law, and fell in the qualifyied immunity category. Part of the problem is there was no legitimate previous case law to work from.

Amendment IV
"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."(Source)

The amendment 4 says that in order to forcibly search a house the police must have a warrant. The warrant must detail, what is to be searched (car, person, house, or everything on the property) and seized (evidence). Mapp v. Ohio (1961) was a landmark case in which it decided that evidence obtained in violation of the fourth amendment was considered impermissible in court.