How is deque implemented?

It sounds really simple, and I have never really given it a thought before. However just now I realised that it is not as straight-forward as I might have led to believe!

A refresher: deque is a data structure that supports O(1) append operations on both ends (head and tail) and O(1) random look-ups.

Hence deque has a similar characteristics as a vector, only better. Wait a minute, how could that be? If deque is simply a doubly linked-list, then random look-ups will be O(N). That's when I realise that I have been so ignorant and oblivious.