How can I be notified when an element is added to the page?

Question

I want a function of my choosing to run when a DOM element is added to the page. This is in the context of a browser extension, so the webpage runs independently of me and I cannot modify its source. What are my options here?

I guess that, in theory, I could just use setInterval() to continually search for the element's presence and perform my action if the element is there, but I need a better approach.