In the last several decades, avian influenza virus has caused numerous outbreaks around the world. These outbreaks pose a significant threat to the poultry industry and also to public health. When an avian influenza (AI) outbreak occurs, it is critical to make informed decisions about the potential risks, impact, and control measures. To this end, many modeling approaches have been proposed to acquire knowledge from different sources of data and perspectives to enhance decision making. Although some of these approaches have shown to be effective, they do not follow the process of knowledge discovery in databases (KDD). KDD is an iterative process, consisting of five steps, that aims at extracting unknown and useful information from the data. The present review attempts to survey AI modeling methods in the context of KDD process. We first divide the modeling techniques used in AI into two main categories: data-intensive modeling and small-data modeling. We then investigate the existing gaps in the literature and suggest several potential directions and techniques for future studies. Overall, this review provides insights into the control of AI in terms of the risk of introduction and spread of the virus.