The warning police must give before questioning someone in custody - and the reason a missing warning suppresses a statement rather than ending a case.
The Supreme Court held in 1966 that a person in police custody must be told, before being questioned, that they may remain silent, that anything they say can be used against them, that they may have a lawyer present, and that a lawyer will be appointed if they cannot afford one. The requirement exists because custodial interrogation is inherently pressured, and the warning is the safeguard against statements produced by that pressure rather than by choice.
Two conditions have to be met together: custody and interrogation. Questions asked when someone is free to leave, and volunteered statements made without any questioning, generally fall outside the rule - which is why the popular belief that an arrest without the warning invalidates the arrest is wrong. The ordinary consequence of a violation is that the statement is inadmissible, not that the prosecution ends.
Invoking the rights has to be done clearly. Courts have held that silence alone is not an invocation and that an ambiguous reference to a lawyer may not require questioning to stop; an unambiguous statement that the person is invoking the right to remain silent, or wants a lawyer, is what triggers the protection.
This is the point at which the general advice and the legal advice agree: ask for a lawyer, say so unambiguously, and stop talking. Whether a statement is admissible is litigated later, on a motion to suppress, and it turns on details of the encounter - where it happened, whether the person was free to leave, exactly what was said - that are far easier to establish soon afterwards than months later.
These directory pages each list at least one currently published law firm. The list is generated when this page loads, so a page whose listings have lapsed drops out rather than becoming a dead link.