Thirty years ago, DBMS stored data on disks and cached recently used data in main memory buffer pools, while designers worried about improving I/O performance and maximizing main memory utilization. Today, however, databases live in multi-level memory hierarchies that include disks, main memories, and several levels of processor caches. Recent research shows that database performance is directly influenced by all levels of the underlying computer hardware and devices. This tutorial aims at (a) explaining why database performance depends on modern processor and memory microarchitectures, (b) surveying and contrasting research on the topic over the past decade, and (c) discussing future research challenges.