Do apps running in the background drain battery, slow down performance, or use cellular data?

I have heard that if you don't kill the apps running in the background, they will drain your battery, slow your other apps down, and could be using your data without any warning. I've looked all over the place for a definitive answer to this, but different people and websites provide conflicting responses and I haven't found any useful information regarding this issue directly from Apple. If anyone knows whether or not having apps constantly running in the background is harmful in anyway (and has a credible resource to back up their claim) let me know and provide a link to the answer if possible.