My Microsoft live email account is not receiving email from people with gmail accounts.

For Outlook.com or Live mail, check these items in order:

1. In Outlook.com, open Settings > Mail > Junk email.
   • Make sure the Gmail sender addresses or the gmail.com domain are not in Blocked senders and domains.
   • Add the sender address or gmail.com to Safe senders and domains.
   • In Outlook.com, messages from safe senders and domains should not be moved to Junk.
2. Check mailbox storage.
   • If Microsoft cloud storage is full, Outlook.com cannot send or receive email.
   • Messages sent while storage was full are bounced back to the sender and are unrecoverable.
3. Check the account state.
   • If the password was changed recently, update it.
   • The account can also be temporarily blocked because of unusual sign-in activity.
   • If sign-in is affected, use the Microsoft account sign-in helper.
4. If the issue is only with this specific mailbox, also check Rules and Forwarding for anything that moves, deletes, or forwards Gmail messages.
5. If Outlook.com support links do not open, sign in to Outlook.com first, then select the ? at the top of the Outlook.com window to open Help.
6. If Gmail messages are still not arriving after the checks above, the problem can be on the sender side.
   • Microsoft may reject incoming mail when the sender’s domain fails authentication checks such as SPF.
   • In that case, the sender must correct their mail configuration.

References:

• Filter junk email and spam in Outlook | Microsoft Support
• Can't send or receive email in Outlook.com | Microsoft Support
• Fixes or workarounds for recent issues on Outlook.com | Microsoft Support
• Hotmail not receiving any emails from any gmail account. - Microsoft Q&A
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• Not receiving most emails all of a sudden - Microsoft Q&A