Dynamicity of Web and its implications on various components of search systems have taken a large attention in the last decade. This course, in the first place, aims to introduce students to the general and wide topic of Web evolution, and then explore a number of issues that is related to temporal aspects of search and IR. We plan to start with an overview of seminal works that shed light on the evolution of Web within time. Next, we will focus on the impacts of this evolution on search and we will essentially focus on indexing of versioned document collections and time-aware retrieval and ranking. We will discuss evolution of search results and invalidation mechanisms for query result caches, and wrap up the course with a review of some recent approaches that aim to predict and search the future!