TeamCity supports the following notifiers:
Notifications regarding specified events are sent via email. Email Notifier can operate on both user and build configuration levels.
Notifications regarding specified events are sent to the Slack messenger. Slack Notifier can operate on both user and build configuration levels.
Displays the status of the specified build configurations and/or the status of the user changes in the user's IDE. Requires a corresponding TeamCity plugin: IntelliJ Platform plugin, Add-in for Visual Studio; which can be downloaded from the My Settings&Tools page. Refer to the Installing Tools section.
You can configure the notifier settings, create, change, and delete notification rules in My Settings & Tools | Notification Rules.