In 2012, Gmail bypassed Hotmail to become the world's largest free email service. If Gmail rejects your emails, you have a problem, whether you're writing to friends, contacting someone on business or sending out bulk email to customers. It's fairly simple to tell if you're on the blacklist, but getting off it may take some work.
Getting the Message
If Google's put you on the blacklist, your network's email servers will tell you. Gmail responds to blacklisted addresses by sending the servers either a 421 error or a 550. The 421 is for temporary problems; 550 indicates a complete block on mail originating from your Internet address. You may need to contact your email provider to research the servers. You can also enter your domain name on a website such as MX Toolbox and see if the site reports a blacklist.
But You're Not a Spammer
Gmail's blacklist exists to cut off spammers from Gmail accounts. If you send out bulk emails to Gmail addresses, Gmail may decide you look like a spammer. That can happen even if it's a business newsletter and everyone receiving it opted in. It can also happen if someone hacks your account and spams people using your address. Of course if you or your company really do send out spam, then you shouldn't be surprised at how Gmail reacts.
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To get off the blacklist, go to Google support and fill out the form for reporting delivery problems. Google will want to know the affected domain, the number of users, the Gmail users you were trying to reach and the headers for the affected emails. Google makes no commitment regarding how long it will take to get a legitimate email off the blacklist. If you don't want to fill out that much detail, there are IT consultants who'll handle it for you.
Once you're off the blacklist, take steps to stay off it. If your email account was hacked to become a spam generator, assign it a tougher password and keep the password secure. If you send out non-spam legitimate bulk mail, apply to Google using its bulk sender form. You can also work through a bulk maill system such as MailChimp.