IGar-
Remote listening is available via:
- An Android or iOS device running the Roku Remote app - device's internal speaker, wired or bluetooth earphones
 - A Roku Voice Remote Pro - wired earphones only
 - An old Roku Gaming Remote (discontinued, no longer available) - wired earphones only
 - [Edited to ad] Bluetooth earphones connected to several current Roku models.  See this Roku article for details including compatible Roku model list.
 
I have been quite pleased with Panasonic ErgoFit Wired Earbuds. I think they sound exceptionally good for inexpensive earphones.  People more knowledgeable will have to give Bluetooth earphone recommendations.
Edited a second time to further correct a misunderstanding on my part (heh heh, I was right in the first place):
As (now) mentioned above, some of recent Roku devices have the capability of connecting to Bluetooth devices directly.   Previously I had referenced an earlier Roku article that was written before the addition of this capability.  It originally stated that Bluetooth earphones cannot be connected directly, however it has now been updated to acknowledge the new capability for some models, with a cross-reference to the Bluetooth earphone article mentioned above. 
My apologies for any misunderstandings my reading of the earlier article may have caused.