Images edited in Photoshop

One more useful info: if you are opening raw files in ACR you can hold down Shift key before clicking on Open Image button which will become Open Object. In this way you will open Smart Object layer which is special kind of layer which will give you option to re-adjust image in ACR by double clicking on smart object thumbnail. You will see ACR window with settings before opening image in Photoshop what is one more advantage. Change settings and click OK to go back to Photoshop. 

I see others mentioned smart objects. I deliberately left that out just to avoid complicating things too much. Get the basic concepts straight first.

A clarification of concepts: A raw file is processed in the Adobe Camera Raw processor. It's not a filter; it's a raw processor. Photoshop can't open raw files, hence, the ACR raw processor is added as a Photoshop plugin. A raw file is just a sensor dump from the camera. It needs to be de-bayered and encoded into an RGB color space.

When done in ACR, the file is opened into Photoshop as a rendered RGB file. This is a one-way street. It is no longer a raw file, and it can not go back. A lot of sensor information has been discarded in this process, in order to produce a usable image. You cannot resave as a raw file from Photoshop. It's a new file.

To save out from Photoshop, just Save As. The native file format is PSD, but TIFF works just as well. It supports all Photoshop functions. Avoid jpeg, it's destructive and a very limited file format not suitable for high-quality work.

A lot of people are confused by the fact that there is also an ACR filter in Photoshop. This is the ACR engine used in a simplified pipeline on an RGB file. The ACR filter cannot be used on raw files, only on processed RGB files.

Now, to go back and re-edit, you have two options. One, you can reopen the file in ACR, pick up where you left off, or start fresh. Or you can reopen the RGB file (TIFF or PSD), and continue working on that.

Camera Raw proper, or the Camera Raw Filter (in Filter > Camera Raw Filter on the menu bar) in Photoshop?

In any case, save the document in Photoshop's own format - PSD - for later editing. Also, you can use the Camera Raw Filter non-destructively on a layer in the document by converting the layer to a Smart Object. (Layer > Smart Objects > Convert to Smart Object on the menu bar). Then you can change settings in the Camera Raw Filter later on even after closing and re-opening the document. (Double-click the filter effect under the affected layer in the Layers panel to change that particular layer's effect.)*

Note that this takes up more memory but that's the price you pay, amirite?  😄

*say that three times fast!

The best option is to save as PSD which will keep image uncompressed with all non-destructive edits. You can use Smart Object layers, adjustments layers, to patch/retouch on separate layers and so on.. When you reopen PSD files everything will be as when file is saved so you can edit image or even to edit your previous edits.