- Where are you living?
- Where have you been living?
Both of them imply you are currently living in a place but what's the real difference between them?
Where are you living?
asks only about present time. It is not concerned with the past at all.
Where have you been living?
asks about some point in the past that extends up to the present. So it is concerned with the past up to the present moment. The point in the past is unknown or left open unless it is stated:
Where have you been living the past three days?
asks about the past three days up until now.
Where have you been living since we last saw each other?
asks about the time period that began when the speaker last saw the listener and ends at the moment of speaking (now).