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With the explosive growth of data available on the Internet, a recent area of investigation called Web Mining has arise. In this paper, we will study general aspects of this area, principally the process of Web Usage Mining where log files are analyzed. These files register the activity of the user when interact with the Web. In the Web Usage Mining, different techniques of mining to discover usage patterns from web data can be applied. We will also study applications of Fuzzy Logic in this area. Specially, we analyze fuzzy techniques such as fuzzy association rules or fuzzy clustering, featuring their functionality and advantages when examining a data set of logs from a web server. Finally, we give initial traces about the application of Fuzzy Logic to personalization and user profile construction.