Database researchers and practitioners have been building methods to store, access, and update data for more than five decades. Designing access methods has been a constant effort to adapt to the ever changing underlying hardware and workload requirements. The recent explosion in data system designs – including, in addition to traditional SQL systems, NoSQL, NewSQL, and other relational and non-relational systems – makes understanding the tradeoffs of designing access methods more important than ever. Access methods are at the core of any new data system. In this tutorial we survey recent developments in access method design and we place them in the design space where each approach focuses primarily on one or a subset of read performance, update performance, and memory utilization. We discuss how to utilize designs and lessons-learned from past research. In addition, we discuss new ideas on how to build access methods that have tunable behavior, as well as, what is the scenery of open research problems.