Starting on Monday, six years after it launched with contactless, Oyster users will finally able to benefit from weekly capping. If your Monday → Sunday fare total exceeds a certain amount, dependent on where you've travelled, you won't pay any more.
Oyster's been able to cope with daily capping for some time, and weekly capping if you only use buses and trams, but weekly capping's previously been too tough to implement on a legacy smartcard which takes payments in real time. They've sorted it now, or at least found a workaround that'll return refunds of a certain size the next time you tap in, hurrah.
Weekly capping is part of TfL's magic farebox which most users don't understand and generally ignore, trusting they'll end up paying the right amount in the end. Calculating the appropriate cap yourself involves keeping track of which zones you've visited, then interrogating a script on the TfL website or finding the right box in a two page table. So here's my simplified summary, assuming you're paying full adult fare and haven't ventured beyond zone 6.
Only used bus or tram
Never travelled in zone 1
Travelled in zone 1 at some point
any 2 zones = £27.70 any 3 zones = £30.70 any 4 zones = £36.80 any 5 zones = £46.30
What you have to be careful of is making one extra journey which messes up your overall cap for the week. For example if you spend Monday to Saturday pootling around Croydon (z5) on buses and trams, then on Sunday take the train up to central London, your cap would almost double. Likewise a weekly commute between Richmond (z4) and Kingston (z6) gets capped at £30.70 so should save you money, but take one train up to zone 1 at the weekend and you'll totally blow it.
Anecdotally the capping system is cleverer than that, scanning all possible caps to find the best fit, so it'd charge my Croydon example as "bus cap + z1-5 return" and my Richmond example as "z4-6 cap + z1-4 journey". But I can find no published evidence that this is actually the case, and you'd only know for sure if it ever happened to you, and most people never hit the weekly cap anyway, which just goes to show how much of a black box the entire fares system is.
None of this is new. But from Monday if you have Oyster rather than contactless, welcome to the world of muddy savings.