Uncertain data are inherent in some important applications, such as environmental surveillance, market analysis, and quantitative economics research. Uncertain data in those applications are generally caused by factors like data randomness and incompleteness, limitations of measuring equipment, delayed data updates, etc. Due to the importance of those applications and the rapidly increasing amount of uncertain data collected and accumulated, analyzing and mining large collections of uncertain data have become an important task and attracted more and more interest from the data mining community. In this tutorial, we will give a systematic survey on the motivations/applications, the problems, the challenges, the fundamental principles and the state-of-the-art methods of mining uncertain and probabilistic data. We will motivate the survey with several interesting practical applications of uncertain data analysis. To set the stage, we will discuss two major models for uncertain and probabilistic data briefly. We will cover several important data mining tasks on uncertain data, including clustering, classification, frequent pattern mining and online analytical processing (OLAP). For each task, we will analyze the challenges posed by uncertain and probabilistic data and the state-of-the-art solutions.