Anne-Sophie F. Mainly just media controls (both for standard Chromecast and for Chromecast Audio) such as play/pause, stop, volume etc. Also with Chromecast you can turn on/off TVs by casting or using Google Assistant (works via HDMI CEC) and so it would be great to be able to trigger this from the remote too, perhaps with the option to use either IR or the Chromecast's HDMI CEC commands to control TV power.
In fact, it might be good to be able to pair an IR device to a chromecast for a combined remote. For instance volume and power IR controls for the connected TV or amp alongside the Chromecast media controls.
If we had voice control from the remote it would also be great to search content to cast by voice.