Overloaded iPhone and iPad mailboxes with excessive new messages

Both iOS machines sport the latest updates, but the amount of Inbox entries is overwhelming -- especially on the phone and on the go. What setting(s) should I change?

[Re-Titled by Moderator]

Original Title: iPhone and iPad mailboxes (in Mail) overload. I get well over 100 messages. But iMac and MacBook Air only report a reasonable 25~30 new.