Hexcrawls, pointcrawls and other options for exploration in D&D

D&D 5e boasts three pillars of gameplay. Combat, Roleplay and Exploration. We’re going to offer some ideas on how to run Exploration for your games.

Narration

If the area is not threatening or if there is nothing of consequence, it’s perfectly fine to tell your players “this area is safe. The roads are maintained by the Queen’s guards, merchants travel these roads in caravans as well as the occasional vendors and inns you’ll encounter along the way. Is there something you want to do on your way to so and so?”
You can introduce some merchants, any npcs that might relay plot points (Oh, you’re heading to the swam of fondue? I heard that there’s a big mean dragon there!), or perhaps the players would want to roleplay some moments when they’re setting up the campfire for the night. Unless there’s…