Each day there is at least one event going on. There are different kind of events with special rewards in each.
The Enchanted Forest event dungeons have many evolve materials of certain a color appearing in them. The first dungeon has low-level evolve materials, and the later dungeons have higher evolve materials. You also need a bit of good luck to find and capture what you're looking for. You also obtain a special chest from the dungeon containing some evolve materials, so make sure you have free chest slots.
There is a special event for capturing Mimics that are also used for evolving.
The Golden Creatures event features many gold heroes that can be captured and then sold for lots of gold. Chests from this event also give you gold.
The Secret Forest event features XP Ghosts that give more XP than regular heroes when used as a fuse sacrifice. These are essential for levelling up your heroes quickly. The chests from this event also contain Ghosts.
The Enchanted Ruins event gives you a chest containing runes, so make sure you have free chest slots. The first dungeon gives lower level runes, and the later dungeons give higher level runes.