While it exists information on about any topic on the web, international evaluation programs in Information Retrieval have shown that some queries are difficult for systems, which means systems fail to answer to these queries in an effective manner. In this talk I will present various methods that are used in order to try to predict if a query is going to be difficult for the system to answer. I will present some analyses regarding system effectiveness according to system configurations and the link with query difficulty. I then present some machine learning techniques used in order to combine predictors of query difficulty. Finally I will depict some users studies conducted to observe how users perceive query difficulty. I will conclude considering some concrete applications of query difficulty prediction.