This chapter will focus on challenges in modeling credit risk for new accounts acquisition process in the credit card industry. First section provides an overview and a brief history of credit scoring. The second section looks at some of the challenges specific to the credit industry. In many of these applications business objective is tied only indirectly to the classification scheme. Opposing objectives, such as response, profit and risk, often play a tug of war with each other. Solving a business problem of such complex nature often requires a multiple of models working jointly. Challenges to data mining lie in exploring solutions that go beyond traditional, well-documented methodology and need for simplifying assumptions; often necessitated by the reality of dataset sizes and/or implementation issues. Examples of such challenges form an illustrative example of a compromise between data mining theory and applications.