Quoting from the Best Practical website:

In other words, it's a powerful, yet simple, open source package to display the Zabbix integration. This is not to say that it is the only issue tracking system that you can use with Zabbix; once the principles behind the following sample implementation are clear, you will be able to integrate any product with your monitoring system.

Request Tracker (RT) is a web application written in Perl that relies on a web server to expose its frontend and on a relational database to keep all its data on. The main means of interaction with the system is through the web interface, but it also features a powerful e-mail-parsing utility that can categorize an e-mail message, turn it into a full-fledged ticket, and keep track of the subsequent mail exchange between the user and the support staff. Closer to our interests, it also features a simple, yet effective, REST API that we'll rely on in order to create and keep track of the existing tickets from Zabbix. On the other hand, a powerful scripting engine that can execute custom chunks of code called scripts not only allows RT to automate its internal workings and create custom workflows, but also allows it to communicate with external systems using any available protocol.

The following diagram shows the basic application architecture. All the data is kept in a database, while the main application logic can interact with the outside world either through the web server or via e-mail and custom scripts.

This is not the place to cover an in-depth installation and configuration of RT, so we will assume that you already have a working RT server with at least a few users and groups already set up. If you need to install RT from scratch, the procedure is quite simple and well documented; just follow the instructions detailed at http://www.bestpractical.com/docs/rt/4.2/README.html. Refer to the Request Tracker website link provided earlier for further information.