What's the reward for completing missions?

You get a mission badge, and there's also a medal called SpecOps that's given after completing unique missions. Levels are:

• bronze: 5
• silver: 25
• gold: 100
• platinum: 200
• onyx: 500

I've not seen any mission give AP on completion.

Update in july

I've done quite a few missions recently, and they indeed gave AP, 125 each. I'm still not sure if it's only a few missions, or they all give.

A badge is given as well as 125AP. I assume that one could consider the items gathered in the hack to be reward. Further of the portal is owned by the enemy a takedown and turning grants you AP. So really it's what you do at these portals during a mission that would bring the outcome

As a traveler and ingress enthusiast, I've found the missions to serve best as "location history". Typically you only do missions (particularly banners and mosaics) when you are in the area for an extended time and want a lasting memory of it on ingress. This gives depth to each agent as you can get a sense of their history without knowing exact details.