Web alerts are user-defined monitor conditions for public Internet information in which notification messages are sent to users whenever their alert conditions are met. The notification conditions are directly or indirectly and completely or partially based on public information available on the Internet such as news, stock prices, exchange rates, oil price, etc. In some alert services, the user can reuse this information to define alert conditions for some required interests in which mobile phone text messages, instant messages, or email alert messages are sent to them upon meeting the pre-specified alert conditions. This paper discusses currently available alert models and some research based proposed models. Then it provides a classification of these different web alert models. This study also provides engineers and researchers with an overview of these models and their types then discusses several system design issues and challenges related to each alert model.