1. To be placed on or supported by something else, especially in a temporary or unusual manner. The television rested precariously upon a wobbly old stool. Sorry, my computer was resting upon some of your papers.

2. To lay or lean something on top of something else, especially gently and temporarily. In this usage, a noun or pronoun is used between "rest" and "upon." You can rest the box upon this stack of magazine while I clear some space on the workbench. Here, rest your leg upon this pillow to help the swelling go down.

3. To recline or lie on something as a means of recuperating. Let me know if you need any help, I'm just going to rest upon the sofa for a little while.

4. To rely, depend, or be contingent on someone or something. A peaceful resolution to this conflict rests upon the two countries' leaders engaging in meaningful, productive talks. You can't just rest upon the success of your first novel to remain relevant with readers, you have to always be striving for bigger and better things.