Magento – Magento 2 Mail Queue / log

This is not a problem of Magento itself.

But if you send mails directly via a mail delivery agent from your webserver, the configuration of this one might be neglected.

I am assuming you send via the standard Linux mail delivery.

You have the following options:

1. configure your mail system on the Magento server to use a well configured mail server for example of your ISP
2. use an extension - AShroder's SMTP Pro module would fit.

One interesting provider which promises (untested) to take a lot of effort that your mail is actually delivered is Amazon SES - the module you mentioned also has a dedicated interface to Amazon SES.

Are you sure that email is not sent? Maybe it's in SPAM or something. Try to send email by simple PHP script:

<?php
 $to = "recipient@example.com";
 $subject = "Hi!";
 $body = "Hi,\n\nHow are you?";
 if (mail($to, $subject, $body)) {
   echo("<p>Email successfully sent!</p>");
  } else {
   echo("<p>Email delivery failed…</p>");
  }

If it don't work configure postfix/smtp/exim server.