The newest update across Android and iOS adds options for playback quality (low, normal, high and always high) over WiFi and for downloaded tracks.
Previously, you could only adjust quality for streaming over mobile data. As 9to5 Google notes however, the selections don't say what bitrate each option corresponds to.
Spotify, for example, offers streams ranging from 96kbps and 320kbps. Tidal goes one step further, offering CD-quality 16-bit encodes.
Apple Music, for its part, simply has a nondescript "high-quality" option. For downloaded music, higher quality will eat up more local storage, while streaming it over WiFi will put a bigger hit on any data cap that may be in place.