Kate Moss is 51 and feeling tons of fun, and we've got all the best shots to celebrate another trip around the sun for the veteran runway model.

The star celebrated her bday earlier this week ... and, while she's a relatively private person who seems to stay off social, her agency -- the Kate Moss Agency -- sent her their best wishes in an IG post.

Moss rose to prominence during the "heroin chic" fashion craze of the 1990s ... appearing in ads with a grungy element to them.

KM gained round the world attention, making millions of dollars each year by modeling ... and, looking incredible in pics -- usually posing with little to nothin on.

Moss has turned toward mogul-ing in recent years ... opening up her agency, contributing to British Vogue as an editor and creating her own clothing range -- though she did jump back on the runway for the Victoria's Secret fashion show back in October!

Moss isn't the only famous member of her family ... her sister Lottie and her daughter Lila have both risen to fame in the modeling world too.

So, happy belated birthday, Kate ... hope you had a super day for a supermodel!