This is one of the most studied problems in computer science, which is just touched in basic algorithm and data structure courses offered at the undergraduate level.This chapter makes a step forward by first introducing universal hashing, which solves some negative issues that basic hash functions experience, and then moves on to describe several advanced approaches to hashing, such as perfect hashing, Cuckoo hashing, minimal ordered perfect hashing, and finally Bloom filters. The theoretical analysis and algorithm description is enriched by figures and pseudocodes, plus several running examples that drive the reader to a better understanding of these important and advanced algorithmic concepts and tools.