Investigating Build Problems
When for some reason a build fails, TeamCity provides handy means of figuring out which changes might have caused the build failure and lets you assign some of your team members to investigate what caused the failure of this build or start investigation yourself. When an investigator is set, he/she receives corresponding notification. A subject for investigation is not necessarily the whole build, it can also be some perticular test. For each project you can find out what problems are currently being investigated and by whom at the dedicated Investigations tab.
To start investigation of a failed build:
Navigate to the Overview tab of the Build Configuration Home page, or Overview tab of the Working with Build Results, click the Start investigation link.
Select team member's name from the User drop-down list and click Assign.
To investigate problem in more than one build configuration, click more and select the desired build configurations.
To start investigation of a particular test, navigate to the Viewing Tests and Configuration Problems of the Build Results page, click the arrow next to the test name and select Investigation.
My Investigations
To view all problems assigned to you to investigate, click a box with a number next to your name. 
Note that for each failed test on this page you can get a bunch of information instantly, without a need to leave this page. For example, you can see all build configurations where this test is currently failing. You can see current stacktrace and information about a build where the test is currently failing. You can also see information about the first failure of this test, again with stacktrace and build.
Since TeamCity 7.1 investigations assigned to you are also highlighted in Web UI, if you have the "Highlight my changes and investigations" option on in your Managing your User Account.