I am not receiving emails about reservation. How to fix it ?

1) Firstly check SPAM / JUNK folder in your mail system.

2) Open Booking > Settings > Emails page and for each email template (switch tabs at toolbar) recheck that you have correct email addresses.

Sometimes mail servers block emails, if the address "From" different from the domain of website, from where this email was sending. Its not really depend from the Booking Calendar. So please open the Booking > Settings > Emails page and recheck that field "From" have the same email as your website domain.
For example: info@your-server.com and not like this your_email@gmail.com
where your-server.com its your website domain.

Also try to set for field "To" in the "New (admin)" email template the same email that you was used in field "From" at this email template page.

Also please be sure that you have activated specific email templates for sending at Booking > Settings > Emails page.
Check-box "Enable / Disable" must be checked at each email template, that you want to use.

3) If you are using paid versions of Booking Calendar, please be sure to configure the email field at the Booking > Settings > Form page, like this [email* email]:

For example:

Email (required):[email* email]

Its default primary email field for booking form!
Please do not use other names for this email field.

4) Check that your PHP mail function is working correctly. You can open your login page and try to retry the password, then check if you received email.

5) This is most common reason of not receiving emails !!!

Try to install the WP Mail SMTP plugin which is 'sending emails via php' option and it can resolve that issue.
If you will have some issue with this plugin, try to install "post smtp" plugin or some other SMTP plugin. Otherwise, please contact support of specific SMTP plugin about correct configuration of settings specific SMTP plugin.

If your emails aren't being received by Gmail, Hotmal, Yahoo Mail accounts, here's information that should help you understand why this is happening.

Issue description
Here is typical situation:
The admin email for your booking system is a “yahoo.com” account.
Customers were receiving emails, if they had a “isp.com” account but not a: gmail.com, hotmail.com, yahoo.com.au

Those emails were rejected by hotmail/yahoo/gmail servers due to their new email policy.
Error logs are showing to refer below links :

If your WordPress is sending emails from some custom email address (for example like this: ‘username@orion-dse.fastwebservers.com.au’), then you needed to enable SMTP authentication with WordPress site so the emails would send from your yahoo/gmail/hotmail email address instead of custom email ( username@orion-dse.fastwebservers.com.au - cPanel default username). This have to fix this issue.

You can fix this problem by installing the “Configure SMTP” WordPress plugin.
You can setup SMTP authentication through any WordPress smtp plugin.
Please refer https://www.youtube.com/watch?v=ZZPfkzEaJaQ
P.S. Thanks to dscottfl about this solution.

6) Please try to test sending of emails by creation of new bookings at front-end side of your website (do not test it from sending test emails at Booking > Settings > Emails page).

7) If the issue still will exist , please try reconfigure Subject and Content of the email template. Make it simpler. May be because of some server restrictions, you are having blocking of sending these emails.

8) Otherwise you can try to use some other mail plugin, like like "SMTP Mail" or "Post SMTP mailer" .

WP Mail SMTP (support: https://wordpress.org/support/plugin/wp-mail-smtp/ )
Post SMTP mailer (support: https://wordpress.org/support/plugin/post-smtp/ )
SMTP Mail (support: https://wordpress.org/support/plugin/smtp-mail/ )

9) Finally, please recheck your error.log and mail.log in your server configuration, about any relative errors.
If you having troubles with checking these files, please contact support of your hosting company about this.