If you go into Device Maintenance under Settings, then to in to the "Battery" category at the bottom and scroll down you will encounter a list, first showing apps that it is suggesting you might want to "Save Power" for, with a button denoting same directly above them. If any of these apps are ones that it's fine to put to sleep leave the check box checked, otherwise uncheck it, then hit the "Save Power" button. It will then "put to sleep" any of the apps you had checked and monitor them in the future once they've been used for putting to sleep after being idle for a while.
Directly under that is a thin dropdown bar that reads, "SLEEPING APPS (XX)", where XX is the number of apps that are being monitored that have been put to sleep by Device Maintenance.
Below that is a button for "Unmonitored Apps" which allows you to create a list of apps that you specifically do NOT wish to have Device Maintenance monitoring at all. You could go into this and add whatever apps concern you as far as possibly missing notifications. I, for instance, added Google Hangouts to that list because my business number is a Google Voice number and if anyone calls me I always want Hangouts to be able to "ring." If it were asleep the call would go straight to voicemail without my ever having known it was coming in.
Then, finally, there is a button for "ALWAYS SLEEPING APPS". This allows you to specifically specify apps that you don't ever wish to have running in the background. In my case, one of those apps is the flashlight app I downloaded that uses the LED camera flash as a steady light when I need it. It need never remain running in the background, consuming any power at all, except when I need it.
That covers about everything you can do within Device Maintenance with regard to the "Battery" category. You can explore the Performance Mode, Storage, and Memory modes if you so desire.