Invoices go out with your bank details on them and customers pay by transfer. You record the payment against the invoice when it arrives, and part payments are supported, so a deposit and a balance both sit against the same invoice.
Card payment
Card payment is not yet built. It is the next significant thing being worked on.
We would rather tell you that plainly than have you move your invoicing across and find out afterwards.
Accounting
There is no automatic feed to accounting software yet either. You can export invoices as CSV for your accountant in the meantime, which most will take happily.