I had an Emirates flight rescheduled last year so that my connection would be blown. They didn't advise me of this at all. I only noticed it when I logged in to Manage My Booking and saw the flight timings had changed.
When I called, I was given the option of taking a longer layover in Dubai at my own expense (to arrive 24 hours later). I wanted to travel the previous day instead so I wouldn't miss my meetings, but they charged me a change fee to do that.
I wrote to Skywards Gold requesting a refund of the change fee but didn't get a response. It was only INR 2000 (US$40) so it really wasn't worth the hassle of complaining.
Compensation? Haha. Surely you jest.