As foundation models expand in scale and societal influence, the ability to faithfully remove undesired data, knowledge, or capabilities has become critical. This challenge, known as machine unlearning (MU), involves the irreversible removal of sensitive data, copyrighted content, and harmful behaviors from trained models. In this chapter, we present MU as both a scientific frontier and a societal necessity. We distinguish it from shallow model editing and emphasize the central triad of challenges: achieving unlearning effectiveness/robustness (erasing the target) and preserving non-target utility to avoid collateral damage. To frame this book, we adopt a tri-design perspective, spanning model, data, and optimization, which together provides the methodological and practical foundations of MU. We also situate unlearning in applied contexts, underscoring its role in AI safety, trustworthy deployment, and compliance-driven governance. MU is not peripheral, but foundational for safe, reliable, and governable AI.