Explore the fascinating world of quantum and classical communication complexity in this 25-minute conference talk. Delve into the differences between interactive two-way communication and simultaneous message passing (SMP) while examining bits, qubits, and their associated complexities. Investigate relations and functions, both partial and total, as you uncover the intricacies of communication complexity as a mathematical model of computation. Learn about the Gap Hamming problem, from its function to its relation, and understand why the Gap Hamming Relation (GHR) is considered challenging for R. Gain valuable insights into this cutting-edge field of computer science and quantum information theory.