Did my email send

To review records of emails you have sent to your customers, open the quote / invoice in question.
Scroll to the bottom and under the header NOTE, are details of the send out. Details include the date and the 'send to' email address. You can click this row to add more notes.
Additionally, you can see at a glance which invoices you have emailed and those you haven’t. Under the Invoices tab (list of all invoices), invoices that have been emailed will display an icon just to the right of the invoice number.

To review emailed Customer Statements (statements generated via Customers > Invoices Estimates & Stats > Statement button at the top of the page):
Go to, Customers > Open the Customer data > Contact Details.
Scroll to the Notes section. Here you'll see information on when and to whom statements have been sent.
If you think you’ve sent the email but there is no record in notes:
Your email has not been sent. Send yourself a test: open the invoice / quote > Email Invoice > swap out client email for your own.
Troubleshooting
If the email sends successfully to yourself… were you originally trying to email multiple people at once? If so, make sure they are formatted with a semi-colon between, for example, abc@kashflow.com; xyz@kashflow.com
If the email does not send successfully to yourself, ensure the address you have entered in Settings > Company Details is correct. Remove any extra spaces and characters not part of the address.
BCC’ing yourself on all e-mails
The best solution to reviewing / keeping a record of emails you have sent to customers is to BCC yourself on all of them. You can do this automatically via Settings >Email Options, Enable the BCC feature and enter the email address you would like to send copies to.
Now you will receive copies of invoices and quotes sent out to your customers in your email Inbox.