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Warrantless entries are limited to those authorized by consent, probation or parole search conditions, or "exigent circumstances" involving some sort of emergency requiring immediate action. One category of exigency that may justify warrantless entry is the need to prevent the imminent destruction of evidence.
Some actions you take have been classified by Supreme Court decisions as requiring that you articulate a "reasonable suspicion" in order to make them constitutionally reasonable, while others can be undertaken only if there is "probable cause" ("PC"). But what do these terms mean? And how do you match the right level of justification with the kind of conduct you're seeking to justify?
When a suspect's vehicle is lawfully impounded (such as when the driver is arrested where the vehicle cannot be safely parked and locked, and there is no sober, licensed driver to take custody of it), it is usually permissible to conduct a standard inventory of the vehicle and its contents.
When you take down a drug house, or enter a home to investigate domestic violence, or serve a search warrant at a residence, which of the multiple people that you sometimes encounter would have the legal standing to challenge the lawfulness of your entry and search?
In the usual case, both the seizure and the search must be reasonable under the Fourth Amendment in order for the evidence to be admissible. The U.S. Supreme Court and federal appeals courts have considered both issues when officers have used K-9s to detect contraband.
Modern surveillance techniques still use the old methods, but technology can make the process both easier and more likely to yield good results.