On an Upcoming, Due, or Overdue invoice you will have the option to record a payment. You can do this by clicking ‘Record a payment’ in the top right toolbar of the invoice.

Clicking this will prompt you to add a payment and note, allowing you to record a full or partial payment on an invoice. 

The payment and the new balance as well as the transaction history are recorded on the invoice, and the balance is also reflected on the main Invoices page.