To see a customer's subscription renewals and payments, click Members > search for the customer and click their name. This will being up their profile, clicking the 'Memberships' tab on their profile page will show all their memberships.
Find the membership in question and you will see all the infomration for that particular member, including the start and expiry dates, billing cycle and payment history and any refund history.
Invoices
Under Payment History, you will see a link icon π - this icon will open up the Stripe invoice/receipt with details of the transaction, handy if you need to send it to the member for any reason.
Example of a member's transaction details.