Saving in photoshop --> illustrator

Saving as a tiff means that you can transfer without the white background. PNG can also do this, but it's more for internet. In tiff, when you save, there is an option to save transparency. Tick this box, and when you place it into illustrator it will not have the white outline.

If you have a layered photoshop document. save it as a psd, making sure that the layers mode is ticked. When you place this into illustrator, DON'T PLACE. Open directly into illustrator, options, convert layers to objects. Default is to flatten image, but if you need the layers intact do it this way.

If you're transferring a vector image into illustrator, if you paste in as a smart object, you can continue editing it. When you double click on this object in photoshop, it automatically reopens in illustrator, can change it there, and when you save it, this automatically changes in the photoshop.