Schemas have always played a crucial role in database management. For traditional relational and object databases, schemas have a relatively simple structure, and this eases their use for optimizing and typechecking queries. In the context of XML databases, things change. Several different schema languages have been defined, tailored for different application classes. Moreover, XML schema languages are inherently more complex, as they host mechanisms for describing highly irregular and flexible structures. In this tutorial we will describe the theoretical models behind these languages, their formal properties, and will also present the complexity of the basic decision problems. We will explore some theoretical and practical applications of schemas for query processing; finally, we will discuss how decision problems can be efficiently solved, at the price of some restrictions on the expressible types.