1. Literally, to trip on something with one's foot. I wasn't watching where I was going and stumbled upon the root of a tree. The child stumbled upon the steps of the house.

2. To find, discover, or happen upon something casually or by chance. I stumbled upon this fantastic little café the other day. Let me know if you stumble upon my keys—I haven't been able to find them. While researching ways of boosting the immune system, the team ended up stumbling upon a remarkable new method of treating cancer.