Though the plugin successfully sends millions of emails every day, there are a host of issues that can stop or delay emails on both the sending and receiving ends. It depends entirely on your local Server & WordPress configuration. You will need to investigate this issue for your particular local configuration.
See Contact Form 7 Email Issues. Most people that work through this information appear to be able to resolve their email sending & receiving issues.
@fezzzz – The Success Message and not receiving any error messages is a very clear indication that CF7 is sending the email.
So your email is probably being seen as spam somewhere in the email process. This is usually due to email headers (in particular the From email address used) or email content.
Emails can be considered spam for a whole host of reasons and get rejected at many points in the email process in addition to your spam folder.
@bilianam2002 – the Yahoo issue has been answered many times in this forum. You can read about what MailChimp thinks of Yahoo’s approach at https://blog.mailchimp.com/tag/dmarc/?utm_source=MonkeyWrench+Newsletter&utm_campaign=60cdb6ad9e-MonkeyWrench_May_2014&utm_medium=email&utm_term=0_6f9c46a454-60cdb6ad9e-87036826