Twilio developer evangelist here.
There aren't specific events for joining or leaving a Conference within Twilio. However, you can find that information out yourself.
Firstly, every time your application responds to a call webhook with a <Conference>
action that is someone joining your conference. You can log the participants and their callSids at this point. You can also call upon the Participants List resource at any time to find out what calls are currently participating in the conference.
As for people leaving, when a user hangs up the phone and you supply an action
attribute to your <Dial>
verb, that action will receive a webhook where you can either continue the call with more TwiML, finish the call or discover if the user hung up using the DialCallStatus
. You can use that callback to infer that someone has left the Conference. Or, you can again use the Participants resource to find out who is in the Conference at this point.
Let me know if that helps at all.