AI systems now match or exceed human performance in areas like face recognition, protein structure prediction, and conversational interfaces, but that progress comes with serious risks. Examples range from coding agents that ignore explicit constraints to widespread use of chatbots for health advice and documented cases where flawed vision systems contributed to wrongful arrests. Explainability is framed as the practical response to this gap between impressive capability and unreliable behavior. The introduction uses concrete cases to show what explanations can uncover: an image classifier calling a husky a wolf because it relied on snowy background, large language models forming cross-modal internal concepts such as the Golden Gate Bridge, and AlphaGo producing moves that first looked bizarre and later became sources of human strategic learning. It also pushes back on common myths, arguing that explainability is especially necessary in high-stakes domains and does not inherently require sacrificing model performance. Even if full understanding of modern neural systems remains out of reach, partial explanations are presented as valuable for trust, scientific insight, and debugging. The session then sets up the rest of the tutorial with historical context, technical deep dives, practical tools, and future directions.