What's a MMO without some quests? The Repopulation has them, but they are not like other MMO's. There are no quest hubs in this game. While there are NPC's who give out quests in the world, they are usually just repeatable bounty missions where you turn in some item for a reward.
The Repopulation give players quests in their PDA/E-Mail system. They are generated automatically based on the zone which the player is in. The player can then accept them, or ignore them. The missions are generated based on all sorts of factors. For example, if I special enemy has spawned in the zone, you'll often see a mission pop up for it. Time of day, npc's and such all factor in to the missions generated. It's a neat system.
Like any good sandbox, this is all optional. I rarely do missions as I am busy with crafting. However, there are crafting/gathering missions to be done if you need a little direction or extra cash. You can also earn abilities through missions. It's a random chance that this will happen, but it is very nice when it does. One of the interesting aspects of it is that you can't see the rewards of the mission until you complete it. Apparently a lot can happen during the mission that can change the reward.