Conversations can't be deleted at the moment, but you can work around this by archiving a private conversation or removing all the participants from a group conversation. Click the options menu (3 dots) and choose Archive conversation for private messages or Edit conversation for group messages.
To remove people from a group conversation, click the “x” next to participants or groups until all are deleted. This will remove the conversation by default. If you find that you are unable to remove yourself from the conversation, you can remove everyone else and then archive it.