Email is occasionally not sending emails?

The other day, a few months ago, both my website and email went down. A few days later all returned to normal, or so I thought. I noticed I wasn't getting any emails, and wondered if it was broken, or if the world simply hated me. I had a few friends send me test emails, which I received. Shortly after I got an email that didn't make sense... I had already sent the stuff they were asking for. Then I realized, the world did not hate me, my email hated me, and emails were not being replied to because emails were not being sent. SOME emails are being sent, and some emails aren't. What is going on???