Engines in Browser - How do they interact?

Okay, so I've been trying to learn more under the hood when it comes to Web Development, specifically Javascript, and how the different engines interact with the Javascript engine. For example, I know that the Rendering Engine is interacting, HTTP Requests, etc. But I guess I'm slightly confused on at what point can another engine start processing asynchronously with the Javascript engine? Let me elaborate a little: You want to render some content in Javascript. How does the data get sent to the render engine? And by the time it gets there, has Javascript completed the current execution context? If so, does the render engine have to syntax parse? Does the render engine compute synchronously as well? I know these are a lot of questions, I feel like I have a good understanding this far so I think it should make sense to those who know this stuff. I know there are some pretty intelligent and generous people on here, I'm reaching out to you, I would appreciate it a lot!