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Ever since the beginning of the Web, finding useful information from the Web has been an important problem. Existing approaches include keyword-based search, wrapper-based information extraction, Web query and user preferences. These approaches essentially find information that matches the user's explicit specifications. This paper argues that this is insufficient. There is another type of information that is also of great interest, i.e., unexpected information, which is unanticipated by the user. Finding unexpected information is useful in many applications. For example, it is useful for a company to find unexpected information bout its competitors, e.g., unexpected services and products that its competitors offer. With this information, the company can learn from its competitors and/or design counter measures to improve its competitiveness. Since the number of pages of a typical commercial site is very large and there are also many relevant sites (competitors), it is very difficult for a human user to view each page to discover the unexpected information. Automated assistance is needed. In this paper, we propose a number of methods to help the user find various types of unexpected information from his/her competitors' Web sites. Experiment results show that these techniques are very useful in practice and also efficient.