Mailblast processes bounce/complaint notifications through Amazon SNS.
Hard bounces and emails marked as spam are automatically filtered in your list, and subscribers will no longer receive emails for future campaigns.
You can see detailed bounce/spam information in each campaigns report:
Note soft bounced recipients are still considered active accounts and are not filtered out in new campaign deliveries. Mailblast will automatically convert subscribers who soft bounce at least 3 times in a 4 week window into hard bounces.