The mission screen itself is further split into four tabs — daily missions (デイリー), main missions (メイン), title missions (称号, see the Trainer title list), and limited missions (限定).
Note that some of the missions in the limited section are in fact available permanently. If you can't find the event you're looking for in the Current Limited Missions, try Permanent Missions.
Current Limited Missions
Daily MissionsMissions available every day. They reset at 5 a.m. JST.
Main MissionsMissions from the Main (メイン) mission tab. As the name suggests, they relate to the general progression through the game, and are always available.
A special type of limited missions that never expire and will only disappear from your list once you've cleared everything from the particular "event".