Hello Hannah, 我没听懂！ 我听不懂！ They are interchangeable in most cases, But 我听不懂！implies that you're way out of your depth when a topic or subject is too difficult or complex for you to understand. When people are talking about Einstein's Relativity... It is too difficult, I don't understand what they're talking about 太难了，我听不懂。( because Einstein's Relativity is beyond your ken, you do not have enough knowledge to be able to understand it.) ...................................................................................................................................................... 我没听懂！would be used more frequently in cases when you didn't listen carefully or you were listening, but half of your attention was somewhere else, or maybe speakers speak too fast for you to follow. When someone is speaking very quickly ... Could you speak a little bit slower? I don't understand what you're saying 能说慢点吗？我没听懂！(it is not beyond your knowledge. you will understand what they're saying if they say it a bit slowly )

我没听懂！ = haven't heard 我听不懂。 = have heard but didn't understand

I think Fenton Benton has perfectly showed the difference between these two phrases. Just want to add one point about WHY these two seemingly nearly same phrases have difference in their meanings. The 没 in 我没听懂！ sort of means "haven't" or "didn't". It indicates the likeliness that I WILL understand if some factors can change a little bit, e.g. speaking speed, another way of explanation. 不 in 我听不懂！ means "don't". It implies that it's not any external factors that hinder me from understanding. It's just I don't have the ABILITY to understand. Hope it helps.

我没听懂！and 我听不懂。I think the main differences are "!" and "。" At the end of the first sentence use "!" ,usually focused on the emotion or the feelings, but the latter sentence just want to state the fact.