A planet in the Solar System that seemed to shrink as the years went by. And another in a distant planetary system that slowly faded into invisibility. And what about shy planets that take time to show their faces? Planetary detective work has been the stock-in-trade of astronomers for centuries, but still provides puzzles that need patience and careful observations to solve. In this fully-illustrated talk, Fred Watson opens up the missing-planets casebook, and explores some of its mysteries.