I am the opposite of a techie, but here I go speaking out of school.
It would be client side. The user could set up a payment X$ every Y period until Z date or on going.
Preferably the intention of payment(subscription) would be held in the blockchain and the merchant could see it. As long as funds are in the account on the right date , the payment goes. It would be nice if the inputs did not have to be there to create the scheduled payment. If that were achieved, then it is just like a real traditional bank account. Your wages go in, and each month your expenses go out.
Only the customer can cancel subscriptions. Merchant has no control over it.
If inputs must be known and "locked" upfront, then it is a lot less useful, but still cool, for 4.99 subscription sites, etc I would like it because I hate subscriptions. I prefer to prepay things. But there are a lot more uses if you do not need the inputs upfront. Likewise it is cooler if the client does not need to be opened once a Y period. That is why it would be great for the intention/subscription to be held on the blockchain.