This chapter deals with the design of compressed data structures, an algorithmic field born just 30 years ago which now offers plenty of compressed solutions for most, if not all, classic data structures such as arrays, trees, and graphs. This last chapter aims at providing just an idea about these novel approaches to data structure design, by discussing the ones that we consider the most significant and fruitful, from an educational point of view. A side effect of this discussion will be the introduction of the paradigm called “pointerless programming,” which waives the explicit use of pointers (and thus integer offsets of four–eight bytes to index arbitrary items, such as strings, nodes, or edges) and instead uses compressed data structures built upon proper binary arrays that efficiently subsume the pointers, and support efficiently/optimally some interesting query operations over them.