Some F1 races have a permanent home while others bounce around, but some have yoyo'ed between two circuits their entire history. The German Grand Prix, for example, has (with few exceptions) been held either at the Nürburgring or Hockenheim. The British Grand Prix alternated between Silverstone and Brands Hatch for decades before the former won out. And in Japan, it's always come down to either Fuji or Suzuka.
Fuji is owned by Toyota and Suzuka by Honda, and the Japanese Grand Prix has always gone back and forth between the two. But these days it's all about Suzuka. With the exception of two years, Suzuka has hosted the race every year since it rejoined the calendar in 1987. Fuji was supposed to alternate like Hockenheim and the Nürburgring, but hasn't hosted since 2008, and now it looks like it won't again for the foreseeable future.
Suzuka has just signed a new contract with Formula One chief Bernie Ecclestone that will see it hosting the race until 2018, putting an end (at least for now) to the prospect of Fuji slipping back into the rotation. The development comes right as the circuit's owner is set to re-enter the series, initially as an engine supplier for McLaren, giving Honda a home race of its own.
The circuit also hosts rounds of the World Touring Car Championship, Super GT and other racing series, while the neighboring Twin Ring Motegi – also part of Honda's Mobilityland Corporation – brings in MotoGP and (until a couple of years ago) the IndyCar Series as well.