As head of state, she is widely valued for her dignity, poise and steadfast dedication to her country.
But according to the Archbishop of Canterbury, many of her subjects fail to appreciate the Queen's wicked sense of humour.
In a video to mark her Diamond Jubilee, Dr Rowan Williams speaks of his personal relationship with the Queen and hails not just her insight and judgment but also her "real personality".
Reflecting fondly on their one-to-one meetings, the bespectacled Archbishop says: "I hadn't had any contact at all with royalty before coming into this job.
"I didn't know what to expect, really. I found in the Queen someone who can be friendly, who can be informal, who can be extremely funny in private - and not everybody appreciates just how funny she can be -, who is quite prepared to tease and to be teased, and who, while retaining her dignity always, doesn't stand on her dignity in a conversation.
"I think we've been enormously fortunate in this country to have, as our head of state, a person who has a real personality."
During the short film, which can be viewed on YouTube, Dr Williams recalls his own encounters with the Queen and speaks of her unswerving support.
"Part of the regular rhythm of life as Archbishop is that I see the Queen privately, just one to one, perhaps once or twice a year," he says.
"I have really valued those meetings because she is always extremely well informed about issues concerning the Church - extremely supportive and full of perception.
"She's seen lots of archbishops come and go, she's seen prime ministers come and go, so she knows something of the pressures of the job.
"And I've always found it really refreshing to be able to talk with her about these questions, to get her perspective - purely personally, I've felt very strongly supported there."
Dr Williams, who will deliver the sermon at the national service of thanksgiving at St Paul's Cathedral on Tuesday, also speaks of the "very great debt" owed to the Queen.
"It seems to me that what her importance has been for most people in this country has been as a sign of stability, a sign of some kind of security," he says.
"And that wouldn't have happened had she not been so profoundly committed at every point, so intelligently committed to understanding the society she was in, working with the flow of the changes that have taken place.
"To have someone who has been a symbol, a sign of stability through all that period is really a rather exceptional gift."