(covers information from several alternate timelines)
Interrogation, also known as questioning, refered to the process of extracting information from a captive. Police often interrogated criminals, and in wartime, opposing sides may interrogate prisoners of war. Interrogation was often part of torture, and an interrogation chair was an aid to interrogation. Truth serums were sometimes administered during interrogations.
Captain Jonathan Archer of the starship Enterprise NX-01 was kept hostage and interrogated by Commander Thy'lek Shran of the Andorian Imperial Guard in June of 2151. This interrogation also included physical torture. (ENT: "The Andorian Incident")
In 2370 of the mirror universe, Elim Garak asked Intendant Kira Nerys to allow him to interrogate a Terran who had been caught stowing away on a ship in order to escape Terok Nor, in order to determine who helped the person do so. That interrogation resulted in the arrest and eventual execution of Quark. (DS9: "Crossover")
In 2371, Enabran Tain asked Elim Garak to interrogate Odo for information regarding the Founders. He used a device which emitted a quantum stasis field to inhibit Odo's ability to change shape. Although Garak was certain that everything Odo knew about the Founders had already been divulged, he nonetheless carried out the interrogation hoping to gain Tain's trust. Unable to change back into his liquid state, Odo began to degenerate until he finally divulged one secret to Garak that he had not revealed to anyone else: he wished to return to his people, the Founders. Ashamed of what he had been doing, Garak deactivated the stasis field, allowing Odo to regenerate and ending the interrogation. (DS9: "The Die is Cast")
The Mari Constabulary on the Mari homeworld interrogated their witnesses and suspects in an interrogation room. In 2374, Chief Examiner Nimira interrogated Kathryn Janeway, Neelix, and B'Elanna Torres in this room where they were placed in a chair opposite the interrogating officer. (VOY: "Random Thoughts")
In 2375 of the mirror universe, Quark, Rom, and Grand Nagus Zek stalled the mirror Garak's attempt to execute them with the Ulcartic virus by negatively comparing him to their Garak and demanding that he interrogate them for information. (DS9: "The Emperor's New Cloak")