Extremely Formal and Diplomatic Contexts: You will encounter 阁下 in formal diplomatic correspondence, official government speeches when addressing foreign dignitaries, or in very solemn written invitations.
Historical Dramas, Novels, and Wuxia: This is where 阁下 truly shines today. It's used constantly in period dramas (古装剧 - gǔzhuāngjù) and martial arts (wuxia) fiction to authentically recreate the formal speech patterns of the past. Characters use it to address officials, respected martial artists, or mysterious figures of great power.
Video Games, Anime, and Fantasy (ACGN): In the world of Anime, Comics, Games, and Novels, 阁下 is frequently used to convey a character's nobility, authority, or archaic nature. A knight addressing their lord, a mage addressing an archmage, or even a villain speaking to a hero with mock formality might use this term. It's often a direct loanword from the equivalent Japanese honorific, `閣下 (kakka)`.
Sarcastic or Humorous Use: Very rarely, and usually among netizens online, it can be used humorously or sarcastically to treat a friend or a situation with mock-seriousness. This is a niche usage and not recommended for learners.