Temper tantrums

What can I say....tantrums are not fun!!! Hannah has been having tantrums in some form or another since she was about 8 months old. Recently though, they have become more frequent. She seems to get frustrated easily because we can't always understand what she wants and because she wants to do more than she can do. She doesn't seem to have the tantrums around Brian. I think she gets tired of being with me all of the time. I'm struggling with whether to just ignore the tantrum or to tell her "No!" so that she knows that isn't acceptable behavior.