Double clicking a graphic style should open a window similar to layer style in photoshop that allows editing that graphic style and gives the option to make the style global (to decide whether edits apply to anything that has the particular style applied or not). Graphic styles could be very useful, but at the moment the panel is very unintuitive. Thanks!

The advantage from making the changes in a menue: you can preview the change which is way more easy to make overall changes.

I added Screenshots of the options I can edit in InDesign when I formated with objectstyles and the option window I see in Illustrator, which just allows me to change the name.

I´m creating a hugh map and now roughly formating the rivers, streets etc. but I know I need to change them later. It would be so easy working with the objectstyles from InDesign... This is such a great and helpful feature!

Hmm. Illustrator allows it with Apperance. and Graphic Styles panels. Are you aware of these?
If you are, and you think they are not sufficient for your tasks — can you please elaborate more on those features of InDesign’s approach you are missing in Illustrator specifically? Please provide details and examples. Thanks!

Einfach, wie in InDesign, Objektformate anlegen können... fixe Kontur- und Flächenfarben und -stärken, Effekte....

Also, why there is still no assignable hotkey for this? Using an action slot for this feels wasteful.

Yes, Redefine works! Thanks, Margaret (if I recall correctly, you even have an action to call this?) Quite hidden, like merging swatches... Still, opening a window/panel/whatever to edit the style chosen can be useful.

if there are possibility to have graphic style editable with all object attributes like object style in inDesign

I would really appreciate the ability to directly change a graphic style definition from the graphic styles menu (like you can in InDesign). Currently the only way to change a graphic style is to edit an object in the Appearance panel, and then use the context menu to redefine the graphic style.

However, there are a number of functions settings in InDesign's object style feature that would be very beneficial to have in Illustrator, such as size of item (so that I could create multiple circles and have the graphic style resize them to the same size, as well as adjusting their appearance).

As Illustrator is an application for creating graphics, it seems logical that it would have options for working with those graphics that are at least as robust as the options available in InDesign. Right now, the graphic styles function in Illustrator is not very robust and of minimal value.

I have attached a screenshot of the Object Style Options menu from InDesign to provide some context for this request. Every item on the left is an area where the Object Style definition can be adjusted to meet the exact needs of the designer.

Areed, although for now I'd at least settle for being able to create, edit and delete graphic styles in extendscript. Then we'd be able to script our way out of the awkward mess graphic styles are currently in.

There's a "redefine graphic style" item in the Appearance palette's menu.