Emails always queued with status 250

My application uses Simple E-mail Service from AWS + GoogleMail for sending mails to clients.

But I have a lot of complaints about mail never received, even after more than 24 hours.

In the logs, I see:

250 2.0.0 Ok: queued as XXXXXXX reportingMTA: a9-82.smtp-out.amazonses.com

Can anyone tell me:

• Is e-mail queued on Amazon OR on recipient server?
• Where can I find rules to help me avoid that?