In this talk, I walk you through adversarial robustness research starting from the early days of synthesizing adversarial attacks all the way to data dependent randomized smoothing for certification. We will cover the early motivations behind adversarial robustness, problem definition, empirical defenses, exact verification and certification through over approximation approaches. We will conclude the talk with the recent probabilistic certification techniques (Randomzied Smoothing) and our latest progress in this direction.