A 2017 update to the answers:

Instead of Oystercards you can now use a bank or credit card which does contactless payments.

The cost will be taken from your bank or charged to your credit card, but in most casees it will work as an Oyster card, sometimes it even gives more advantages.

As already mentioned in the accepted answer, instead of Oystercards you can use a bank or credit card which does contactless payments.

The cost will be taken from your bank or charged to your credit card, but in most casees it will work as an Oyster card, sometimes it even gives more advantages.

When the other answers were written it was relatively new and restricted but these days it is rather common and the options in public transport in London are broader than they used to be.