Their father, Takanohana I, was an Ozeki, and their uncle, Wakanohana I, was a Yokozuna. Takanohana I retired shortly after his defeat by a Yokozuna named Chiyonofuji.
Eleven years later, when Takanohana was 18 years old, he defeated Chiyonofuji. Two days later, Chiyonofuji retired. At the time, Chiyonofuji joked that one day, his son (then 5) might come to upset Takanohana.
I might add that, in addition to his history and skill, Takanohana's popularity was helped by the fact that he is really cute.